A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Answers
C's 1 days work
=1/3 - (1/6 + 1/8)
= 1/3 - 7/24
= 1/24
A wages:B wages:C wages
1/6:1/8:1/24
C shares for 3 days
= ( 3 × 1/24 × 3200)
=400
Given :- A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days.
To Find :- How much is to be paid to C ?
Solution :-
→ LCM of 6 , 8 and 3 = 24 units = Let total work .
so,
→ Efficiency of A = Total work / days = 24/6 = 4 units/day.
→ Efficiency of B = Total work / days = 24/8 = 3 units/day.
→ Efficiency of (A+B+C) = Total work / days = 24/3 = 8 units/day.
then,
→ Efficiency of C = Efficiency of (A+B+C) - Efficiency of A - Efficiency of B = 8 - 4 - 3 = 8 - 7 = 1 units/day.
we can conclude that,
The payment was given in the ratio of their Efficiency .
therefore,
→ C received = (1/8) * 3200 = Rs.400 (Ans.)
Hence, Rs.400 is paid to C .
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