# 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