Question

A and B can do a piece of work in 21 and 24 days respectively. They started the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?

Answer 1

Hey.

Here is the answer.

As A can do the work in 21 days

so, 1 day work of A is 1/21

similarly 1 day work for B is 1/24

let A leaves the work after x days

so, work done by both in x days = x/21 +x/24

B works for 9 days alone so work done in 9 more days by B

= 9/24

According to question;

x/21 +x/24 +9/24 = complete one work =1

or, (24x + 21x + 189)/ 504 = 1

or, 45 x = 504 -189 = 315

or, x = 315/45 = 7

So, after 7 days A left.

Thanks.