Question

A and B can do a piece of work in 54 days and 48 days respectively.
They began the work together but A leaves after some days and B finishes
the remaining work in 31 days. After how many days did A leave the work?​

Answer 1

Step-by-step explanation:

First Method:

A takes 54 days of work.

B takes 48 days of work.

LCM = (54, 48) = 432/48 = 9

Efficiency of A = 432/54 = 8

Efficiency of B = 432/48 = 9

B finishes remaining work on 31 days

i. e, 31 × 9 = 279 work is done by B.

Remaining work is 432 - 279 = 153

153 work is done by A and B.

They take 153/17 days (9 + 8 =17) efficiency.

They take 9 days to work together.

So, A leave after 9 days

Second Method:

A can do work in 54 days.

So, in one day A does (1/54) part of work.

B does (1/48) part of work.

So together, in one day they do ((1/54)+(1/48)) part of work.

Now, B does 1/48 part of work in one day. So, in 31 days B will do 31/48 part of work.

Remaining work: (1-31/48) = 17/48 part.

(17/48) part has been done by both A and B

initially.

Now,

A & B together do ((1/54)+(1/48)) part of work in 1 day

So, 17/48 part will be done in = (17/480/((1/54)+ (1/48)) days = 9 days

So, after 9 days A left the work.

Third Method:

Total work to be done LCM(54,48)=432 parts

So A does 432 parts in 54 days so A does 432/5458 parts/day

Similarly B does 9 parts/day

Together they do 17 parts/day

Let they work together for d days after which A left

So they do 17xd parts

Now B does remaining work in 31 days

So 17xd +31x9= 432

d = 9

So A left after 9 days

Cheers ☺

Have a nice day ☺

Answer 2

Step-by-step explanation:

Hope my help will help you.