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54. (b)  If the price of a commodity increases by R%, then the
                     +
                           +
                 Mon Tues Wed
                                    °
        49. (b)                  =  37 C           ...(1)             reduction in consumption. So as not to increase the
                        3
                                                                      expenditure is
                     +
                           +
                 Tues Wed Thur   =  34 C                               é  R       ù      9
                                     °
                        3                          ...(2)              ê  ë  100 R  ´  100 % =  ú  û  100 9 ´  100
                                                                           +
                                                                                          +
                 Subtracting equation (2) from (1)                    = 8.25%
                 Mon – Thurs = 37 × 3 – 34 × 3
                                                              55. (d)   Pupils from first school appeared for an examination
                 5   Thus – Thurs = 9                                 = 80% of 65 = 52
                 4                                                    Pupils from second school appeared for an examination
                 Thurs = 36°C                                         = 52 + 4 = 56
        50. (c)  Let ‘x’ be the sum invested in the bank.             Total pupils in second school = 65 + 10 = 75
                 According to question
                                                                                            56
                           ´
                  ´
                               ´
                      ´
                 x 10 1 +  x 12 1 =  1650                             Pass % of second school =   75 ´ 100  = 74.6%
                   100      100
                                                              56. (c)  1 : 10  could not be the ratio of black to white marbles.
                 10x + 12x = 165000
                 22x = 165000                                 57. (c)  Going by options,
                 x = ` 7500                                           If the total sum is 6400 then distribution among P, Q
                                                                      and R was 1200, 3800 and 1400.
                                 1
        51. (a)  Let sum = ` x, S.I. =  x                             After giving 200 to Q by R.
                                 9
                                                                      New sum would be 1200, 4000 and 1200.
                 Rate = R%
                 Time =  R yrs.                                       Or, 1200 : 4000 : 1200 = 3 : 10 : 3
                          ´
                       ´
                 1  x =  x R R                                58. (b)  Tea 1         Tea 2
                 9      100                                             10            14
                  2
                 R =  100                                                      11
                       9
                 R = 3.33%
                                                                         3              1
                   8%             10%
        52. (a)                                                       Hence, the  ratio should be 3 : 1.


                          9.2%                                                        æ   Rate ö  Time
                                                              59. (b)  Amount = Principal  1+  ç  ÷
                                                                                      è   100 ø
                 0.8%              1.2%
                                                                            æ
                 The ratio in which money lent is 0.8 : 1.2 or 2 : 3  = 1250 1+  4 ö  ÷  2
                                                                            ç
                 Therefore, money lent at 10%                               è  100 ø
                   3                                                          26 26
                 =  ´  10000 =  6000                                  =  1250´  ´
                   5                                                          25 25
        53. (c)  Let the total number of votes enrolled be x.         = ` 1352
                 Then, number of votes cast = 60% of x        60. (a)  Let the sum lent at 6% be ` x and that lent at 4% be
                 Valid votes = 96% of (60% of x)                      ` (3200 – x). Then,
                 75% of [96% of (60% of x)] = 7344
                                                                        ´
                                                                           ´
                                                                       x 6 1   (3200 x 4 1-  ) ´
                  75  ´  96  ´  60  ´  x =  7344                        100  +     100     =  176
                 100 100 100
                                                                      6x + 4 × 3200 – 4x = 17600
                             ´
                                 ´
                         ´
                    7344 100 100 100                                  2x = 17600 – 4 × 3200
                 x =
                           ´
                              ´
                        75 96 60                                      2x = 17600 – 12800 = 4800
                                                                      x = ` 2400
                 x = 17000
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