7087363-Solved-Quantitative-Aptitude-Paper-of-Bank-PO by nuhman10

VIEWS: 123 PAGES: 6

									                                                     SPECIAL SUPPLEMENT


                              .O.
                        Bank P Examination Special-III
                                            MOCK TEST
                         Quantitative Aptitude & Reasoning
                            Based on “Latest” Pattern
                   Quantitative Aptitude                               How much per cent of the total students do not get
                                                                       scholarships?
     1. Which of these numbers is rational?                                (a) 68                                    (b) 75
    (a) π                                (b)             (0.04)−1           (c) 79.8                                 (d) 82.5
                                                                            (e) 78.5
    (c)   3
              −1                               (d)   3
                                                         0.8
                                                                              7. If the diameter of a wire is increased by 10%, by how
    (e)   4   0.00016                                                  much per cent approximately, will its length be decreased, if
       2. For the equation px2 + px + q = 0, the value of the          the volume remains the same?
discriminant is zero. The roots of this equation are:                       (a) 15             (b) 16                (c) 17
     (a) imaginary                                                         (d) 18              (e) 19
     (b) irrational                                                           8. There are two numbers R and S, related by the
     (c) rational and unequal                                          equation R = S2. Now, if S is increased by 10%, what will
     (d) rational and equal                                            happen to R?
     (e) real and equal                                                    (a) R increases by 10%
       3. The sum of two times one natural number and three                (b) R decreases by 10%
times another natural number is less than 24. If the first natural          (c) R increases by 21%
number is less than or equal to eight, the highest value of the             (d) R decreases by 21%
second natural number is:                                                   (e) R remains unchanged
     (a) 5              (b) 6                 (c) 7                           9. Mr X gets a salary of Rs 1,44,000 p.a. Assuming the
     (d) 8              (e) 9                                          salary to be the same every month, what will happen to his
       4. A shopkeeper bought 800 kg rice at Rs 3840. He had           average income per day?
to sell it at a loss of as much as he received for 16 kg. The               (a) Maximum for (Jan, Feb, March) period
selling price (per kg, in Rs) will be:                                      (b) Maximum for (Feb, March, April) period
     (a) Rs 40          (b) Rs 100            (c) Rs 50                     (c) Minimum for (July, Aug, Sep) period
     (d) Rs 80          (e) Rs 65                                           (d) All three above are true
                          9 8 5    7                                        (e) Both (b) and (c) above
      5. The fractions     ,  , and can be arranged in                        10. The value of log10 16 – 3 log10 2 + log10 5 is:
                         14 13 7   9
                                                                                  1                                         1
the descending order as:                                                    (a)                                     (b) 1
                                                                                  2                                         2
          7 5 9 8
    (a)    , ,  ,                                                            (c) 0                                  (d) 1
          9 7 14 13
                                                                             (e) 2
          5 9 8 7
    (b)    ,  ,  ,                                                             11. A cistern is two-third full of water. Pipe A can fill
          7 14 13 9                                                    the remaining part in 12 minutes and pipe B in 8 minutes.
           9 5 8 7                                                     Once the cistern is emptied, how much time will they take to
    (c)     , ,  ,
          14 7 13 9                                                    fill it together completely?
          7 9 5 8                                                            (a) 12 minutes
    (d)    ,  , ,                                                            (b) 12 min, 12 sec
          9 14 7 13
                                                                             (c) 14 min, 24 sec
           8 9 5 7                                                           (d) 10 min, 12 sec
    (e)     ,  , ,
          13 14 7 9                                                          (e) 14 min, 40 sec
     6. The boys and girls in a school are in the ratio 3 : 7.                 12. Which inequations are represented by the shaded
25% of the boys and 20% of the girls are scholarship holders.          area shown in the graph?

                                                 1139 s JULY 2002 s THE COMPETITION MASTER
                                                                           SPECIAL SUPPLEMENT

                                             4                                                  water must be evaporated from it so that the solution now
                                             3                                                  contains 25% salt?
                                             2                                                       (a) 54                (b) 45                     (c) 36
                                             1                                                       (d) 27                (e) 18
                                                                                                     20. Mr Mohit is 7 times as old as his son. 10 years hence
                                                  1    2    3   4
                                                                                                he will be 3 times as old as his son. What are their present
                                                                                                ages (in years)?
                                                                                                     (a) 4, 28             (b) 5, 35                  (c) 3, 21
                                                                                                     (d) 6, 42             (e) 7, 49
                                                                                                     Directions (Q. 21-25): Study the following bar-graph and
     (a) x > 0, y > 0                       (b) x > 0, y ≥ 0                                    answer the questions (21-25) given below. (The diagram shows the
     (c) x > y, y > 0                       (d) x = y, y < 0                                    sale of six garment companies in three successive financial years.)
     (e) x ≥ y, y ≥ 0                                                                                                                                 1998-99          1999-2000                2000-2001
                                                                                                                                100
     13. There are 7 points in a plane, no three of them being                                                                  90
collinear. The number of triangles formed by using these points                                                                 80
                                                                                                                                                 80

is:




                                                                                                        Sales in Rs. (Crores)
                                                                                                                                70          66               68
                                                                                                                                                                                 63
                                                                                                                                                                                                60
     (a) 7                  (b) 21                  (c) 10                                                                      60
                                                                                                                                                                  52
                                                                                                                                                                            57             57
                                                                                                                                50
     (d) 4                  (e) 35                                                                                                     44               46
                                                                                                                                                                                                          40
                                                                                                                                                                                                               43   46
                                                                                                                                                                                                                         40
                                                                                                                                40
     14. In how many ways can we arrange 6 books on                                                                                                                    33             34
                                                                                                                                                                                                                              30
                                                                                                                                30
different subjects, in a shelf?                                                                                                 20
                                                                                                                                                                                                     20
     (a) 6                (b) 60            (c) infinite                                                                        10
     (d) 720              (e) 120                                                                                                0
                                                                                                                                      Ramu & Co. Shyamu                Champa Motu Bhai               Lambu         Dabbu Bhai
     15. The recurring decimal 2. 345 can be expressed in the                                                                                     & Co.                Garments & Brothers           Tewari &        & Sons
                                                                                                                                                                                                     Brothers
rational form as:                                                                                    21. Which of the following garment companies has a
          2343                                                            2345                  fluctuating sales figure over the given period?
    (a)                                                             (b)
           990                                                             999                       (a) Lambu Tewari and Brothers
          2343                                                            2345                       (b) Dabbu Bhai and Sons
    (c)                                                             (d)                              (c) Motu Bhai and Brothers
           999                                                             99
                                                                                                     (d) Champa Garments
          2345
    (e)                                                                                              (e) Shyamu and Company
          1000
                                                                                                     22. What is the total percentage increase in the sale of
    16. If a =       4                  6              3
                         9,b=               26 , c =       5 , then, which of these             garments in 2000-2001 with respect of 1999-2000?
statements is true?                                                                                  (a) 4% fall                           (b) 4% rise
     (a) 4 9 < 6 26 <           3                                                                    (c) No change                         (d) 7% increase
                                    5
                                                                                                     (e) 5% decrease
    (b)   4          6          3
              9 >        26 >        5                                                               23. For the total 3-year period under consideration, the
    (c)   6
              26 >   3
                         5 >    4
                                    9                                                           nearest competitor of Ramu and Company is:
          6          3          4                                                                    (a) Champa Garments
    (d)       26 <       5 <        9
                                                                                                     (b) Motu Bhai and Brothers
    (e) None of these                                                                                (c) Shyamu and Company
                                                            x 2 + 7x + 10                            (d) Dabbu Bhai and Sons
    17. The value of the expression                                            is:
                                                            x 2 + 2x − 15                            (e) None of these
                                                                                                     24. For the years 1998-99 and 1999-2000, which company
          x+5                            x+2                              x−3
    (a)                        (b)                                  (c)                         has the minimum rate of change of sales?
          x−3                            x−3                              x+2
                                                                                                     (a) Dabbu Bhai and Sons
          x+5                               x+2                                                      (b) Lambu Tewari and Brothers
    (d)                         (e)
          x+2                               x+5                                                      (c) Ramu and Company
                1      1                                                                             (d) Champa Garments
    18. If 3      x + 2 x = 64 – 2x, then x equals:                                                  (e) None of these
                2      2
                                                                                                     25. For the years 1999-2000 and 2000-2001, which
    (a) 8                (b) 7                    (c) 6                                         company has the maximum rate of change of sales?
    (d) 5                (e) 4                                                                       (a) Dabbu Bhai and Sons (b) Ramu and Company
    19. A 90 kg salt solution has 10% salt in it. How much                                           (c) Shyamu and Company (d) Lambu Tewari and Sons

                                                                          1140 s JULY 2002 s THE COMPETITION MASTER
                                                   SPECIAL SUPPLEMENT

     (e) Champa Garments                                                   (a) 32         (b) 36                (c) 35
     26. A train running at the speed of 90 km/hr crosses a                (d) 30         (e) 38
platform of length 160 m in 10 seconds. What is the length of              35. How many girls are there in science stream of school
the train (in metres)?                                                D?
     (a) 60            (b) 90             (c) 150                        (a) 264            (b) 704             (c) 88
     (d) 140           (e) 40                                            (d) 264            (e) Data inadequate
     27. The average of 4 consecutive even numbers is 9.                 36. A square is inscribed inside a circle of radius 4 cm.
Which of these is the first number?                                   What is the area of the shaded region in the diagram?
     (a) 6             (b) 4              (c) 8
     (d) 10            (e) 12
     28. The distance between Charu’s and Mani’s places is
120 km. Charu travelled the whole distance from her place to
Mani’s at 30 km/hr but returned at 40 km/hr. Her average
speed for the whole journey is (approximately):
     (a) 36 km/hr      (b) 37 km/hr       (c) 33 km/hr
     (d) 34 km/hr (e) 35 km/hr
     29. The average of the 1st 50 natural numbers is:                                                                      20
     (a) 25            (b) 25.5           (c) 26.4                         (a) 10 cm2         (b) 8 cm2               (c)      cm2
                                                                                                                             3
     (d) 50            (e) 50
                                                                           (d) 16 cm2         (e)   8 cm
                                                                                                         2

     30. A certain sum of money doubles in 10 years at simple
                                                                           37. A square is drawn inside a right-angled triangle with
interest. What is the rate of interest?
                                                                      the two perpendicular sides as 12 cm and 8 cm. What is the
     (a) 20%            (b) 30%              (c) 10%
                                                                      side of the largest possible square that can be drawn?
     (d) 5%             (e) 12%
                                                                           (a) 4 cm          (b) 4.8 cm           (c) 4.5 cm
     Directions (Q. 31-35): Study the pie-chart and table given
                                                                           (d) 4.4 cm        (e) 5 cm
below and answer the questions that follow—(The data shows
                                                                           38. Three terrorists are employed to shoot a reknowned
statistics about 4 schools (A, B, C and D) as in the year 2001.)
                                                                      person Mr X. Only one bullet is sufficient to kill him if it
                                   Students’ Ratio                    strikes in the head. The probabilities of the terrorists striking
                                School Science :    Boys :            Mr X’s head by their bullets are 0.2, 0.3 and 0.4. What is the
                                     Commerce :     Girls             probability that Mr X is shot dead?
                                         Arts                              (a) 0.336         (b) 0.9              (c) 0.1
                                   A    1:4:1        5:4
                                   B    4:1:1        5:1                   (d) 0.760         (e) 0.664
                                   C    2:5:2        2:7                   39. Which of the following numbers is a perfect square?
                                   D    3:5:1        1:8                   (a) 10201         (b) 12222            (c) 11112
                                                                           (d) 55555         (e) 10101
     31. Which school has the maximum number of girl                       40. The following two figures have the same perimeter.
students?
     (a) A             (b) B                 (c) both C and D
     (d) C             (e) D
     32. If the number of students of school A increase by
12.5% and that of school B decrease by 10%, what is the ratio
of the number of students in the two schools?
                                                                                     Square                  Circle
     (a) 2 : 3         (b) 3 : 2             (c) 1 : 1
     (d) 4 : 3         (e) 3 : 4                                          Which of the following statements is true?
     33. In school B, 10% students failed in science, 20% failed          (a) The square and the circle have equal areas.
in commerce and 30% failed in arts. What is the percentage of             (b) The area of square is greater than that of the circle.
failures in school B?                                                     (c) The area of the circle is greater.
     (a) 15            (b) 25                (c) 12                       (d) Area of circle is π times that of the square.
             1                                                            (e) None of these.
    (d) 12            (e) 17
             2                                                            41. Prasoon’s bike needs a fresh paint. He wants 2 shades
    34. The total number of arts students expressed as a              on his bike. The painter shows all the available 5 shades. In
percentage of total number of commerce students is                    how many ways can Prasoon paint his bike?
(approximately):                                                          (a) 7             (b) 10               (c) 25
                                                                                                  2
                                                                          (d) 20            (e) 5
                                                1141 s JULY 2002 s THE COMPETITION MASTER
                                                  SPECIAL SUPPLEMENT
     42. A bag contains 4 white and 3 black balls. 2 balls are         and answer the incomplete series (B), in the following questions.
drawn out one at a time, randomly in succession. What is the           Assume that series B follows the same rule as series A.
probability that both the balls drawn out are white in colour,             48. Series A: 12        24 48 96 192
if the first ball is replaced before the second draw is made.                  Series B: 0.5 x          y     z      t
          9                  4                   12                        What should come in place of t?
    (a)               (b)                  (c)
          49                12                   49                        (a) Both (d) and (e)          (b) 4              (c) 84.5
          4                 16                                             (d) 8                        (e) 180.5
    (d)               (e)                                                  49. Series A: 2         5    17 71 ...
          7                 49
                                                                               Series B: 1         a    b     c
    43. What is the maximum value of the function
                                                                           What will replace the symbol b?
        f(x) = x2 + 5x + 16
                                                                           (a) 47                (b) 11                 (c) 3
          16                4
    (a)               (b)                  (c) 16                          (d) 17                (e) 12
           5                3
                                                                           50. Series A: 2         11 47 128 ...
          39                25                                                 Series B: 5         m n        o     ...
    (d)               (e)
           4                16                                             The value of n is ...
     44. On giving a reduction of 20% on clothes, a cloth-                 (a) 27                (b) 50                 (c) 25
merchant’s sale increased by 30% to become Rs 26,000 in the                (d) 21                (e) 62
month of June 2002. What was the previous sale?
     (a) Rs 25,000                          (b) Rs 30,000                          Answers (with Hints and Solutions)
     (c) Rs 13,000                          (d) Rs 24,500
     (e) Rs 20,000                                                      1. (b)     (0.04)−1 =
                                                                                                100
                                                                                                    = ±
                                                                                                        10 FG IJ
     45. The difference between the product of two numbers                                       4       2  H K
and their sum is 24. What is the difference between the two             2. (e) If D = 0 → the roots are real and equal
numbers?
     (a) 24                                                             3. (c) We can write: 2x + 3y < 24
     (b) 25                                                                    The highest value of second can take place when the
                                                                                first is having lowest value.
     (c) Data inadequate
     (d) Several solutions                                                      Lowest value of 1st = 1
                                                                                                      (Q smallest natural number = 1)
     (e) None of these
     46. Mr Sanjay Sharma, Mr Pravesh Khare and Mr Mitra                       Thus, 2(1) + 3y < 24
are partners in a business. Mr Mitra started the business with                                3y < 22
Rs 40,000. After 3 months, Mr Sanjay and Mr Pravesh joined                                           22
                                                                                                y<      ~ 7
him with Rs 60,000 each. If the total profits at the end of the                                       3
year amount to Rs 31,200, what would be Mr Khare’s share in             4. (a) Let SP per kg be Rs x
it?                                                                            → Total SP = 80 x and loss = 16 x
     (a) Rs 15600                           (b) Rs 9600
                                                                               Now, loss = CP – SP
     (c) Rs 10800                           (d) Rs 21600
                                                                               → 16x = 3840 – 80x
     (e) None of these
     47. Mr Rajiv and Mr Jogesh can complete a piece of work                   i.e. x = 40
in 6 days and 8 days respectively. They started together but            5. (a) By cross-multiplication (or otherwise), compare the 4
                                                                                                     7 5  9   8
Rajiv left the work after 2 days. In how many days will Mr                       fractions. Thus,     > >   >
Jogesh complete the remaining work now?                                                              9 7 14 13
            3                                                                                              25(3x)    20
    (a) 4 days                                                          6. (e) Scholarship holders =              +     (7x)
            4                                                                                               100     100
            2                                                                                              3x 1      43x
    (b) 2     days                                                                                     =     + .7x =
            3                                                                                               4 5       20
            1                                                                    Total = 3x + 7x = 10 x
    (c) 4     days
            2                                                                                                  F 43x I
                                                                                 % of scholarship holders =    GG 20 JJ     × 100 = 21.5
    (d) 4 days                                                                                                  GH 10x JK
            1
    (e) 3 days
            3                                                                    ∴ % of those without scholarships = 78.5
    Directions (Q. 48-50): Study the given series (A) carefully         7. (c) V1 = V2 → π × 100 × 100 × l1 = π × 110 × 110 × l2

                                                 1142 s JULY 2002 s THE COMPETITION MASTER
                                                                       SPECIAL SUPPLEMENT
                           l2  100                                                                     x = 5 and father’s age = 7 × 5 = 35 years
                         → l =                                                                 21. (e) Shyamu and Company—It first registered a growth
                            1  121
                                                                                                       and then a fall in the sales.
                                      21
       ∴ % decrease =                    × 100 ≅ 17                                            22. (c) Sum of sales figures in both the years are the same i.e.
                                     121                                                                328 crore each
 8. (c) R = S2                                                                                 23. (c) The total sales of Ramu and Company is Rs 200 crore
                                                                        S               11             which is closest to Rs 166 crore of Shyamu and
        S increases by 10% and becomes S +                                       i.e.      S
                                                                       10               10             Company.
                                                        11 2 121 2                             24. (a) For Dabbu Bhai and Sons, the rate of change is only
       Since R = S2 → R becomes (                          S) =     S                                   46 − 40      6
                                                        10      100                                             i.e.
                                                                                                          46         46
        → % increase in R = 21%
                                                                                               25. (a) For Dabbu Bhai and Sons, the rate of change is
 9. (e) February has 28 days while July and August have 31                                              40 − 30 1
        days. Find average using number of days.                                                               =
                                                                                                          40     4
                                                      16 × 5
10. (d) Given expression = log10 (                           ) = log10 10 = 1                          For others it is less than this.
                                                        8
                                                                                               26. (b) Refer June issue for direct formula on TRAIN problems
                                          1
11. (c) Pipes A and B fill
                                          3
                                            tank in 12 and 8 minutes
                                                                                                      10 =
                                                                                                                FG IJ
                                                                                                             18 x
                                                                                                                 H K
                                                                                                              5 90
        → They fill the whole tank in 36 and 24 minutes
                                                                                                       x = 250 → length = 250 – 160 = 90 m
                          1     1    5
       1 minute’s work =    +     =                                                            27. (a) Let the first number be x
                         36 24 72
                                                                                                              x + (x + 2) + (x + 4) + (x + 6)
                      72                                                                              Then,                                   =9
                                                                                                                             4
       → Time taken =    minutes = 14.4 minutes
                       5
                                                                                                       → 4x = 36 – 12
                       = 14 minutes, 24 seconds                                                              24
12. (e) Refer special P.O. Exam issues of THE COMPETITION                                              → x=     =6
                                                                                                              4
        MASTER (May and June 2002)
13. (e) 7C3 = 35 (Refer May and June issues of CM)                                                                         2 × 30 × 40 2400
                                                                                               28. (d) Average speed =                =     = 34.33 km/hr
14. (d) 6P6 or ∠6 = 720 (Refer May and June issues of CM)                                                                    30 + 40    70
15. (c)                                                                                                                                      n
16. (b) LCM of 4, 6, 3 is 12                                                                   29. (b) Sum of 1st n natural numbers is         [a + l]
                                                               1 12
                                                                                                                                             2
        Thus,        4
                         9 = 9  bge j14
                                            bg
                                          = 9    3 12
                                                        = 93           =    12
                                                                                 729                   Where n = number of terms, a= 1st term, l = last term
                                                                                                                       n
                           16               2 12          2 1 12                                                         [a + l ]   a + l 1 + 50
        6
         26 = b 26g = b 26g = e 26 j                               =   12
                                                                            676
                                                                                                       Thus, average = 2          =      =       = 25.5
                                                                                                                          n           2      2
                                13           4 12         4 1 12
       and 5 = b 5g = b 5g
                 3           = e5 j                                =   12
                                                                            625                30. (c) S.I. = Amount – Principal
                                                                                                       → S.I. = 2P – P = P
       ∴    12
                 729 >     12
                                676 >      12
                                                625
                                                                                                                     PTR      P × 10 × R
17. (b) Factorise by splitting the middle term                                                        Now, S.I. =        → P=
                                     (x + 2)(x + 5)    (x + 2)                                                       100         100
        Thus, we have:                               =
                                     (x + 5) (x − 3)    (x − 3)                                                           → R = 10%
18. (a) Solve as simple linear equations.                                                      31. (d) First put all the data in a relevant form
                                                  10                                                   From the pie-chart, we get,
19. (a) Quantity of salt = 90 ×                      = 9 kg                                                   20          3600
                                                 100                                                   A=        × 3600 =      = 720
                                                                                                             100           5
        If ‘x’ kg water is evaporated,
                                                          FG 9 IJ × 100 = 25                                  25          3600
                                                           H 90 − x K                                  B=
                                                                                                             100
                                                                                                                 × 3600 =
                                                                                                                           4
                                                                                                                               = 900
        Thus, x = 54                                                                                          33
20. (b) Let the son be x years old and father be 7x years old                                          C=        × 3600 = 1188
                                                                                                             100
         Their ages after 10 years are (x + 10) and (7x + 10)
         Thus, according to the question, we have                                                             22
                                                                                                       D=        × 3600 = 792
                                        (7x + 10) = 3(x + 10)                                                100
                                                                   1143 s JULY 2002 s THE COMPETITION MASTER
                                                                       SPECIAL SUPPLEMENT

    Now, dividing the students as per the table, we have:
                                                                                                                                       = π
                                                                                                                                          FG 2xIJ =FG 4 IJ x
                                                                                                                                                2
                                                                                                                                                           2
                  School Science : Comm. : Arts
                  A(720)    120 / 480 / 120
                                                            Boys : Girls
                                                             400 / 320
                                                                                                                                           H π K H πK
                  B(900)    600 / 150 / 150                 750 / 150                                           4
                  C(1188)   264 / 660 / 264                 264 / 924                                 Since       > 1 → Area of circle > Area of square
                  D(792)    264 / 440 / 88                   88 / 704                                           π

32. (c) 12.5% increase in A = 720 + 90 = 810                                                41. (d) (Refer April 2002 issue of CM for more details on the
        10% decrease in B = 900 – 90 = 810                                                          topic of permutations and combinations).
                                810                                                                 Using arrangements or permutations, we have
          Ratio =                   =1:1=1                                                           5          5! 5 × 4 × 3 !
                                810                                                                      P2 =      =           = 20
                                                                                                                3!     3!
33. (a) Number of failures
                   10          20          30                                               42. (e) (Refer May 2002 issue of CM for more details on
          =           × 600 +     × 150 +     × 150                                                 probability).
                  100         100         100
                                                                                                    Required probability = p (1st white) × p (2nd white)
          = 60 + 30 + 45 = 135                                                                             4      4    16
                       135                                                                            =       ×      =
          % failures =     × 100 = 15                                                                     4+3   4 + 3 49
                       900
                                                                                                                                b2        ( 5 )2        25 39
34. (b) Required percentage                                                                 43. (d) Maximum value = c              = 16 −        = 16 −   =
                                                                                                                                4a           4          4   4
                  120 + 150 + 264 + 88
          =                             × 100                                                        (of ax2 + bx + c)
                  480 + 150 + 660 + 440
                                                                                                                                       100 100
             622                                                                            44. (a) Required figure = 26,000 ×            ×    = Rs 25,000
          =      × 100 = 36 (approx.)                                                                                                   80 130
            1730
                                                                                            45. (c) Let the two numbers be x and y
35. (e) The given data only provides the number of students                                         It is only given that xy – (x + y) = 24
        in the 3 streams and the ratio of boys to girls in a                                        We need at least two equations to solve for the two
        particular school.                                                                          unknown variables
                            1 2 1
36. (b) Area =                × r = × 4 2 = 8 cm2                                           46. (c) Money will be divided according to the time and
                            2      2                                                                investment ratios
          (Solve using Pythagoras’ theorem)                                                         Thus, required ratio
37. (b)           A                                                                                             = 40,000 × 12 : 60,000 × 9 : 60,000 × 9
                      8-x
                                                                                                                = 48 : 54 : 54 = 8 : 9 : 9
                  X                     Y                                                                                      9
              8             x                                                                        Mr Khare’s share =            × 31200 = Rs 10800
                                                                                                                             8+9+9
                      x             x
                                                                                                                              1 1 7
                  B             x                       C                                   47. (e) Their 1-day work =         + =
                                        Z        12-x                                                                         6 8 24
                                            12

      The triangles AXY and YZC are similar                                                                       7
                                                                                                      ∴ They do 2 24
                                                                                                                      FG IJ work in 2 days
          Thus, we have:
                          x
                             =
                               12 x                                                                                    H K
                         8−x     x                                                                                               14   5
                                                                                                      Remaining work = 1 –          =
        i.e., x2 = 96 – 20x + x2                                                                                                 24 12
        i.e., x = 4.8 cm                                                                                                               5     10
38. (e) (Refer May issue of CM for a more systematic approach                                         Days taken by Jogesh =             ×8=
                                                                                                                                      12      3
         to this topic)
         Required Probability = 1– q1 q2 q3 (Where q = proba-                                48. (a) We can have two possibilities           × 2, × 2, × 2 ...
                                 = 1– 0.8×0.7×0.6 bility of fail-                                                                            + 12, + 24, + 48 ...
                                 = 1– 0.336       ing to strike)                                     Thus, both (d) and (e)
                                 = 0.664                                                    49. (b) The series A is: ×2 + 1, × 3 + 2, × 4 + 3 ...
39. (a) (101)2 = 10201                                                                               Thus, 1 × 2 + 1 = 3, 3 × 3 + 2
40. (c) Let side of square be ‘x’ cm, i.e. perimeter = 4x cm                                        = 11, 11 × 4 + 3 = 47 etc
                                                                                   2x       50. (b) The given series A is: +32, +62, +92, etc
          Since perimeters are same → 4x = 2 π r i.e. r =
                                                                                   π                 Thus, series B is: m = 5 + 32 = 14,
          Now, Area of square = x2 and area of circle                                                                 n = 14 + 62 = 50, etc

                                                                      1144 s JULY 2002 s THE COMPETITION MASTER

								
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