A, B and C can complete a piece of work in 10, 12 and 15 days respectively. They started together but A left 2 days after the start and B left 3 days before the completion of the work. How long did the work last? MCQ with Answer and Explanation
A, B and C can complete a piece of work in 10, 12 and 15 days respectively. They started together but A left 2 days after the start and B left 3 days before the completion of the work. How long did the work last?
A. 8 days
B. 6 days
C. 7 days
D. 5 days
Answer: Option C
Solution (By JKSSB Mock Tests)
Total work = LCM(10, 12, 15) = 60 units. Efficiency of A = 6, B = 5, C = 4. Let total days be x. A works for 2 days. B works for (x - 3) days. C works for x days. Total work = 2*6 + (x - 3)*5 + 4*x = 60 => 12 + 5x - 15 + 4x = 60 => 9x - 3 = 60 => 9x = 63 => x = 7 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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