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