Question

A alone can do a work in 12 days, B alone in 10 days. A and B undertook to do it
for Rs. 4000. With the help of C, they completed the work in 3 days. How much
is to be paid to C?​

Answer 1

Explanation:

C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 1 .

3 6 8 3 24 24

A's wages : B's wages : C's wages = 1 : 1 : 1 = 4 : 3 : 1.

6 8 24

C's share (for 3 days) = Rs. 3 x 1 x 3200 = Rs. 400

Answer 2

Given :-

• A alone can do a work in 12 days .
• B alone in 10 days.
• A and B undertook to do it for Rs. 4000.
• 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 12 , 10 and 3 = 60 units = Let total work .

so,

→ Efficiency of A = Total work / days = 60/12 = 5 units/day.

→ Efficiency of B = Total work / days = 60/10 = 6 units/day.

→ Efficiency of (A+B+C) = Total work / days = 60/3 = 20 units/day.

then,

→ Efficiency of C = Efficiency of (A+B+C) - Efficiency of A - Efficiency of B = 20 - 5 - 6 = 20 - 11 = 9 units/day.

we can conclude that,

• The payment was given in the ratio of their Efficiency .

therefore,

→ C received = (9/20) * 4000 = Rs.1800 (Ans.)

Hence, Rs.1800 is paid to C .

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