A and B can do a piece of work in 10 days and 15 days respectively. They work together for 2 days and then A is replaced by C. The work is finished in next 4 days. In how many days can C alone finish the work? MCQ with Answer and Explanation
A and B can do a piece of work in 10 days and 15 days respectively. They work together for 2 days and then A is replaced by C. The work is finished in next 4 days. In how many days can C alone finish the work?
A. 8 days
B. 10 days
C. 15 days
D. 12 days
Answer: Option B
Solution (By JKSSB Mock Tests)
Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. In 2 days, A and B do 2 * (3 + 2) = 10 units. Remaining work = 30 - 10 = 20 units. This is completed by B and C in 4 days, so combined efficiency of B and C = 20 / 4 = 5 units/day. Since efficiency of B = 2, efficiency of C = 5 - 2 = 3 units/day. Time taken by C alone = 30 / 3 = 10 days.
A can finish a work in 10 days and B in 15 days. B starts the work and is joined by A after 5 days. What is the total number of days taken to complete the work?
Explanation:
Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. B works alone for 5 days: work completed = 5 * 2 = 10 units. Remaining work = 30 - 10 = 20 units. Now A and B work together with efficiency = 3 + 2 = 5 units/day. Time taken for remaining work = 20 / 5 = 4 days. Total time = 5 + 4 = 9 days.
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