Question

A and B can finish a work in 30 days they worked for it for 20 days and then B left the remaining work was done by alone in 20 more days a alone can finish the work in​

Answer 1

A could finish the whole work in 60 days

Explanation:

Both A and B can finish the work in 30 days.

That means both A and B can finish 1/30 part of the work in 1 day.

So in 20 days, both A and B can finish 20/30 = 2/3 part of the work.

Both A and B worked together for 20 days and completed 2/3 part of the work. Now 1/3 part of the work is remaining.

But after 20 days B left the work. Now A finished the remaining 1/3 part of the work alone.

Given A has completed the remaining 1/3 part of the work in 20 days. We are asked to find in how many days A could finish the whole work.

Let A could finish the whole work in x days.

That means A could finish 1/x part of the work in 1 day.

So in 20 days, A could finish 20(1/x) = 20/x part of the work.

But it's given that A finished the remaining 1/3 part of the work in 20 days.

Thus we are able to equate 20/x and 1/3.

`\longrightarrow(20)/(x)=(1)/(3)`

`\Longrightarrow\underline{\underline{x=60}}`

Hence A could finish the whole work in 60 days.