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 26 days. how long the bot will take to complete work alone

Answer 1

Let the work done by a man in 1 day be x and work done by a boy in 1 day be y

a man and a boy can complete a work in 24 days

=> 24x + 24y = 1 ---(1)

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

=> if a man work for 26 days and a boy work for 20 days, work will be completed

=> 26x + 20y = 1 ---(2)

Solve (1) and (2) for y

(1)*13 gives 312x + 312y = 13 ---(3)

(2)*12 gives 312x + 240y = 12 ---(4)

(3)-(4)=> 72y = 1

y = 1/72

work done by a boy in 1 day = 1/72

A boy alone needs 72 days to complete the work