"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 ₹ 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Answers
Answer:
Step-by-step explanation:
A does (1/6)th and B does (1/8)th of the work in 1 day.
C does (1/3)-(1/6)-(1/8) = (8–4–3)/24 = 1/24th of the work in a day.
A:B:C = (1/6):(1/8):(1/24) or 4:3:1
4x+3x+x = 8x = 3200, or x = 400
So A gets Rs.1600, B gets Rs.1200 and C get Rs.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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