Question

A man and a boy can complete a work together in 24 days.if for the last six days man alone does the work then it is completed in 26days.how long the boy will take to complete the work alone

Answer 1

Heya!

Here's your answer! ^^

Time taken if the man and boy work together to complete the work = 24 days

Their 1 day work = 1/24

ATQ, for the last six days, man alone does the work then it is completed in 26 days.

So, man and boy work together for 20 days.

man and boy's 20 days work
= 20 × 1/24
= 20/24
= 5/6

Remaining work = 1 - 5/6 = 1/6

Then, 1/6 of work is completed by a man in 6 days.

i.e man's 1 day work = 1/36

1/36 + boy's 1 day work = 1/24

Boy's 1 day work = 1/24 - 1/36 = 1/72

∴ the boy alone can complete the work in 72 days

Hope it helps :D