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