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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 C?
₹800
₹400
₹375
₹600
₹400
Find the individual 1-day work rates: A′s1-day work=61, B′s1-day work=81, and (A+B+C)′s1-day work=31. Subtract A and B's rates from the total rate to find C's 1-day work, then distribute the ₹3,200 in proportion to their daily work rates.
A alone can do the work in 6 days (A=6 days), B alone in 8 days (B=8 days), and together with C they can complete it in 3 days (A+B+C=3 days). Total payment for the work = ₹3,200.
Work=Efficiency×Time
Find the individual 1-day work rates: A′s1-day work=61, B′s1-day work=81, and (A+B+C)′s1-day work=31. Subtract A and B's rates from the total rate to find C's 1-day work, then distribute the ₹3,200 in proportion to their daily work rates.
Do not divide the total amount by 3 people equally. Wages must be distributed strictly in the ratio of their daily work efficiency (amount of work done per day).
Calculate Total Work using LCM
Let the total work be the LCM of the given days (6,8,3), which is 24 units.
Total Work=LCM(6,8,3)=24 units
Find Individual Efficiencies (1-day work)
A's 1-day work = 24/6=4 units. B's 1-day work = 24/8=3 units. Combined (A+B+C)'s 1-day work = 24/3=8 units.
EA=4,EB=3,EA+B+C=8
Calculate C's Efficiency
Subtract A and B's efficiencies from the total combined efficiency to find C's 1-day work.
EC=8−(4+3)=1 unit/day
Determine C's Share of Wages
Wages are distributed in the ratio of their efficiencies (4:3:1). C's share is calculated out of the total amount of ₹3,200.
C’s Share=4+3+11×3200=81×3200=400
B is correct because C's share of the wages based on his work efficiency is ₹400.
In work and wages problems, always distribute the total payment in the exact ratio of the daily work done (efficiencies), not the number of days worked.
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