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 : 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