Question

2 men and 5 boys can do a piece of work in 4 days, while 4 men and 4 boys can do it in 3 days.How long it would take one man alone to do it and how many days ity would take one boy to do it alone?

Answer 1

boys rate = 1/b
men's rate = 1/m

job done by 2 men and 5 boys in 4 days
= 4(2/b + 5/m) = 8/b + 20/m

job done by 4 men and 4 boys in 3 days
= 3(4/m + 4/b) = 12/m + 12/b

8/b + 20/m = 12/m + 12/b
8/m = 4/b
8b = 4m
m = 2b or b = m/2
The man's rate is twice the boy's rate.

job = 12/m + 12/b
= 12/(2b) + 12/b = 18/b
= 18(1/b)

One boy alone would take 18 days

Answer 2

Perfect ! Thanks May God bless you :)