A can do a piece of work in 10 days, B in 12 days and C in 15 days. They carry out the work together and get a total of Rs. 4500 as wages. Find the share of C.
Explanation:
Total work = LCM(10, 12, 15) = 60 units. Efficiency of A = 6, B = 5, C = 4. Ratio of wages = 6 : 5 : 4. Total ratio parts = 15. Share of C = (4 / 15) * 4500 = 4 * 300 = Rs. 1200.
Explanation:
Total work = LCM(8, 12, 6) = 24 units. Efficiency of (A+B) = 3, (B+C) = 2, (A+B+C) = 4. Efficiency of C = (A+B+C) - (A+B) = 4 - 3 = 1. Efficiency of A = (A+B+C) - (B+C) = 4 - 2 = 2. Combined efficiency of A and C = 2 + 1 = 3. Time taken by A and C together = 24 / 3 = 8 days.
A can do a piece of work in 20 days and B in 30 days. They work together for 7 days and then both leave. Then C alone finishes the remaining work in 10 days. In how many days can C alone finish the full work?
Explanation:
Total work = LCM(20, 30) = 60 units. Efficiency of A = 3, B = 2. Combined efficiency = 5 units/day. In 7 days, work done = 7 * 5 = 35 units. Remaining work = 60 - 35 = 25 units. C takes 10 days to do 25 units, so efficiency of C = 25 / 10 = 2.5 units/day. Time taken by C for full work = 60 / 2.5 = 24 days.
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