Question

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?

Answer 1

A=6 Total work=24
B=8
A+B+C=3
A efficiency =4
B---------------=3
A+B+C-------=8
A+B+C-(A+B)=1
C efficiency =1
A : B : C
4 : 3 : 1
8=3200
1=800
then C=800

Answer 2

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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