A and B can do a piece of work in 10 days, B and C in 12 days, and C and A in 15 days. How long will C alone take to complete the work? MCQ with Answer and Explanation
A is 50% more efficient than B. C does half of the work done by A and B together in the same time. If C alone can do the work in 30 days, then A, B and C together can do the work in:
Explanation:
Let efficiency of B = 2, then efficiency of A = 3. Combined efficiency of A and B = 5. Efficiency of C = 5 / 2 = 2.5. Total work = Efficiency of C * Time of C = 2.5 * 30 = 75 units. Combined efficiency of A, B and C = 3 + 2 + 2.5 = 7.5 units/day. Time taken together = 75 / 7.5 = 10 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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