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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 ₹3,200. With the help of C, they completed the work in 3 days. How much is to be paid to B?
₹800
₹1,200
₹1,400
₹600
₹1,200
Calculate individual efficiencies by finding the inverse of days. The share of wages is directly proportional to the work done (efficiency) by each individual.
A alone finishes work in 6 days, B alone in 8 days. Total work with C takes 3 days. Total wages = ₹3,200.
Ratio=DaysA1:DaysB1:DaysC1
Calculate individual efficiencies by finding the inverse of days. The share of wages is directly proportional to the work done (efficiency) by each individual.
Students often divide the total money by the number of days directly instead of finding the daily work efficiency first.
Calculate efficiencies
Let total work = LCM(6, 8, 3) = 24 units. A's efficiency = 24/6 = 4 units/day. B's efficiency = 24/8 = 3 units/day. A+B+C's efficiency = 24/3 = 8 units/day.
EfficiencyC=8−(4+3)=1 unit/day
Determine share ratio
The wages are divided in the ratio of the work done by each. A, B, and C work for 3 days each, so the ratio of work done is the same as the ratio of efficiencies.
Ratio=4:3:1
Calculate B's share
Total parts = 4 + 3 + 1 = 8. B's share = (B's parts / Total parts) * Total amount.
Bshare=83×3200=1200
B is correct because the calculated share for B is ₹1,200.
This concept is identical to Pipe and Cistern problems where efficiency ratios determine the flow rate or filling capacity.
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