# 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

## 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