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? MCQ with Answer and Explanation
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?
A. 9 days
B. 6 days
C. 7 days
D. 8 days
Answer: Option A
Solution (By JKSSB Mock Tests)
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.
A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
Explanation:
Total work = LCM(10, 50) = 50 units. Efficiency of (A + B) = 5, efficiency of C = 1. Total efficiency of (A + B + C) = 5 + 1 = 6. Given A = B + C. So, (B + C) + B + C = 6 => 2(B + C) = 6 => B + C = 3. Since C = 1, B = 2. Time taken by B alone = 50 / 2 = 25 days.
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