The ratio of efficiency of A is to C is 5:3. The ratio of no.of days taken by B is to C is 2:3. A takes 6 days less than C, when A and C completes the work individually. B and C left the work after 2 days. The no of days taken by A to finish the remaining work ?



The ratio of efficiency of A is to C is 5:3. The ratio of no.of days taken by B is to C is 2:3. A takes 6 days less than C, when A and C completes the work individually. B and C left the work after 2 days. The no of days taken by A to finish the remaining work ?

A. 4.5

B. 5

C. 6

D. 28/3

Answer : C. 6


Explanation:

  • A : C
      Efficiency of A and C = 5 : 3
      The Ratio of Work done is 3 : 5 = 3x : 5x

      Given:
      Difference between A's and C's work done is 6 days so,
      5x - 3x = 6
      x = 3
      Number of days taken by A = 3 * 3
      = 9 Days
      Number of days taken by C = 5 * 3
      = 15 Days
  • B : C
      Ratio of work done of B and C = 2:3
      As we have calculated C's total work done in 15 days so,
      3x = 15 days
      x = 5
      Therefore, Number of days taken by B = 2 * 5
      = 10 Days
      Now we have total work done by a ,b and c in 9, 10 and 15 days respectively
      Work done by B and C in initial 2 days = 2 * [ 1/10 + 1/15 ]
      = 1/3
      Thus, Remaining work = 1 - 1/3
      = 2/3.

  • A do total work in 9 days so, 2/3 work is done in (9 * 2/3) = 6 days


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