Question

A can do a piece of work in 40 days and B in 45 days. They work together for 10 days and then B goes away. In how many days will A finish the remaining work?

Answer 1

Given,

 A can do a piece of work in 40 days

 B can do it in = 45 days

A’s 1 day work \(=\frac{1}{40}\)

B’s 1 day work \(=\frac{1}{45}\)

(A+B)’s 1 day work togethe \(=[\frac{1}{40}+\frac{1}{45}]\)

A+B’s 10 day work \(={10}[\frac{1}{40}+\frac{1}{45}]=\frac{17}{36}\)

Remaining work \(={1}-\frac{17}{36}=\frac{19}{36}\)

∴ Remaining work will be done by A \(\frac{\frac{19}{36}}{\frac{1}{40}}=\frac{19}{36}\times{40}=\frac{190}{9}={21}\frac{1}{9}\) days