104. A can do a piece of work in 10 days. B can do the same work in 15 days. They worked together for 4 days and then they both left the work. C joins to finish the remaining work. If C alone can finish the work in 12 days, then how much time will he take to finish the remaining work?
(a) 2 days (b) 3 days (c) 4 days (d) 6 days
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Answer:
Total work = 10 unit
Efficiency of A = 1 unit/day
Work done by A in 4 days = 4 unit
Remaining work = 10 - 4 = 6 unit
Let efficiency of B be x, then
9x = 6
⇒ x = 6/9
⇒ x = 2/3
Efficiency of B = 2/3 units/day
Total efficiency of A and B = 1 + 2/3 = 5/3
∴ A and B alone can complete the whole work in = 10/(5/3) = 6 days
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