A can do a work in 11 days and B in 23 days. In how many days will they complete 75% of the work together? MCQ with Answer and Explanation
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Question #1
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A is twice as fast as B. If A and B together can complete a piece of work in 8 days, in how many days can A alone complete it?
Correct Answer: Option D
Explanation:
Let efficiency of B = 1, then efficiency of A = 2. Combined efficiency = 3 units/day. Total work = 8 * 3 = 24 units. Time taken by A alone = 24 / 2 = 12 days.
Let efficiency of B = 1, then efficiency of A = 2. Combined efficiency = 3 units/day. Total work = 8 * 3 = 24 units. Time taken by A alone = 24 / 2 = 12 days.
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Maths
Time and Work
Question #2
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A, B and C can complete a piece of work in 10, 12 and 15 days respectively. They started the work together, but A left after 2 days and B left 3 days before the completion of the work. Find the total duration of the work.
Correct Answer: Option B
Explanation:
Total work = LCM(10, 12, 15) = 60 units. Efficiency of A = 6, B = 5, C = 4. Let the work last for x days. A works for 2 days: work = 12 units. B works for (x - 3) days: work = 5(x - 3). C works for x days: work = 4x. Total work = 12 + 5x - 15 + 4x = 60 => 9x - 3 = 60 => 9x = 63 => x = 7 days.
Total work = LCM(10, 12, 15) = 60 units. Efficiency of A = 6, B = 5, C = 4. Let the work last for x days. A works for 2 days: work = 12 units. B works for (x - 3) days: work = 5(x - 3). C works for x days: work = 4x. Total work = 12 + 5x - 15 + 4x = 60 => 9x - 3 = 60 => 9x = 63 => x = 7 days.
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Maths
Time and Work
Question #3
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A, B and C can do a piece of work in 20, 30 and 60 days respectively. If A works everyday and is assisted by B and C together on every third day, then in how many days will the work be completed?
Correct Answer: Option A
Explanation:
Total work = LCM(20, 30, 60) = 60 units. Efficiency of A = 3, B = 2, C = 1. Day 1: A works = 3 units. Day 2: A works = 3 units. Day 3: A+B+C work = 3 + 2 + 1 = 6 units. Work done in 3 days = 3 + 3 + 6 = 12 units. Number of 3-day cycles to complete 60 units = 60 / 12 = 5 cycles. Total days = 5 * 3 = 15 days.
Total work = LCM(20, 30, 60) = 60 units. Efficiency of A = 3, B = 2, C = 1. Day 1: A works = 3 units. Day 2: A works = 3 units. Day 3: A+B+C work = 3 + 2 + 1 = 6 units. Work done in 3 days = 3 + 3 + 6 = 12 units. Number of 3-day cycles to complete 60 units = 60 / 12 = 5 cycles. Total days = 5 * 3 = 15 days.
This question belongs to:
Maths
Time and Work
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