Question

A can do piece of work in 80 days. He work at it for 10 days and them B alone finishes the remaining work in 42 days. In how many days could both do it? ​

Answer 1

Answer:

If they worked together from the beginning, they would need 30 days to complete the work.

Step-by-step explanation:

Let the total amount of work is 1 unit.

In 80 days A alone does 1 unit amount of work.

In 1 day A alone does 1/80 unit amount of work.

So, in 10 days A alone does 10/80 unit = 1/8 unit amount of work.

After 10 days of working of A alone the remaining amount of work is (1 - 1/8) = 7/8 unit of work.

In 42 days B alone does 7/8 unit amount of work.

So, in 1 day B alone does 7/(8*42) unit = 1/48 unit amount of work.

In 1 day A and B together do [(1/80) + (1/48)] unit = 1/30 unit amount of work.

1/30 unit amount of work is done in 1 day when A and B work together.

So, total work = 1 unit amount of work is done in 30 days when A and B work together.