A can do a work in 6 days and b in 8 days. with the help of a boy, they complete the work in 3 days and get rs.200/-. what is the boy’s share if the money is distributed in ratio of work done by them?
Answers
The boy's share is 44.44 if the money is distributed in the ratio of work done by them.
‘A’ can do a work in 6 days and ‘B’ in 8 days. with the help of a boy, they complete the work in 3 days and get Rs. 200/-.
We have to find the boy's share if the money is distributed in the ratio of work done by them.
Let a boy can do the same piece of work in x days.
if A , B and a boy work together, they can complete the work = 1/(1/6 + 1/8 + 1/x) days
but Given, with the help of a boy , A and B can complete the work in 3 days
∴ they complete the work = 1/(1/6 + 1/8 + 1/x) = 3
⇒1/3 = 1/6 + 1/8 + 1/x
⇒1/3 = (8 + 6)/48 + 1/x
⇒16/48 - 14/48 = 1/x
⇒4/48 = 1/x
⇒x = 12 days
hence, A boy can do the same piece of work in 12 days.
∴ Ratio of number of days taken by A , B and Boy = 6 : 8 : 12 = 3 : 4 : 6
“Efficiency is inversely proportional to number of days taken to do the work.”
∴ Ratio of efficiencies of A , B and Boy = 1/3 : 1/4 : 1/6 = 4 : 3 : 2
so the boy's share = 2/(4 + 3 + 2) × 200
= 400/9 = Rs. 44.44