Question

A can do 1/3 of a work in 30 days. B can do 2/5 of the same work in 24 days. They worked together for 20 days. C completed the remaining work in 8 days. Working together A, B and C will complete the same work in:

A. 15 days
B. 10 days
C. 18 days
D. 12 days

Answer 1

A's work rate is 1/90 work per day, B's is 1/60 per day, and C's is 1/18 per day. Working together, their combined rate is 1/90 + 1/60 + 1/18 = 1/15 work per day. Hence, A, B, and C together can complete the work in 15 days.

Step-by-step explanation:

We are given that A can do 1/3 of the work in 30 days, which means A can complete the entire work in 90 days. B can do 2/5 of the work in 24 days, which means B can complete the entire work in 60 days (since 24 days is 2/5 of the time B needs to finish the work).

To find out the rates of A and B, we take the reciprocals of these times. A's rate is 1/90 work per day and B's rate is 1/60 work per day. When they work together, their combined rate is 1/90 + 1/60 = 1/36 work per day.

A and B together worked for 20 days, hence they completed 20/36 of the work. So, 16/36 (or 4/9) of the work remains. C completes this in 8 days, meaning C's rate is (4/9) / 8 = 1/18 work per day.

To find out how long it would take for all three, A, B, and C, to complete the work together, we sum their rates: 1/90 + 1/60 + 1/18 = 1/15 work per day. Therefore, working together, they will complete the work in 15 days.

The answer is A. 15 days.