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 ?

Answer : C. 6

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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