If 5 men can complete a work in 6 days, and 10 women can complete the same work in 5 days, in how many days can 5 men and 5 women complete the work together?
Explanation:
Efficiency of 5 men = 1/6. Efficiency of 10 women = 1/5, so efficiency of 5 women = 1/10. Combined efficiency of 5 men and 5 women = 1/6 + 1/10 = (5 + 3) / 30 = 8 / 30 = 4 / 15. Time taken together = 15 / 4 = 3.75 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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