A can complete a work in 17 days and B in 22 days. If both work together, in how many days will the work be completed? MCQ with Answer and Explanation
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Question #1
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A can complete a piece of work in 14 days and B in 21 days. They begin together but A leaves 3 days before the completion of the work. Find the total number of days taken to complete the work.
Correct Answer: Option B
Explanation:
Total work = LCM(14, 21) = 42 units. Efficiency of A = 3, B = 2. Let total days be x. A works for (x - 3) days, B works for x days. 3(x - 3) + 2x = 42 => 3x - 9 + 2x = 42 => 5x = 51 => x = 51/5 = 10(1/5) days.
Total work = LCM(14, 21) = 42 units. Efficiency of A = 3, B = 2. Let total days be x. A works for (x - 3) days, B works for x days. 3(x - 3) + 2x = 42 => 3x - 9 + 2x = 42 => 5x = 51 => x = 51/5 = 10(1/5) days.
This question belongs to:
Maths
Time and Work
Question #2
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A can complete a work in 30 days and B in 22 days. If both work together, in how many days will the work be completed?
Correct Answer: Option B
Explanation:
Combined rate = 1/30 + 1/22. Time = 12.69 days.
Combined rate = 1/30 + 1/22. Time = 12.69 days.
This question belongs to:
Maths
Time and Work
Question #3
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A and B can do a work in 12 days, B and C in 15 days, and C and A in 20 days. How many days will A alone take to finish the work?
Correct Answer: Option C
Explanation:
Total work = LCM(12, 15, 20) = 60 units. Efficiency of (A+B) = 5, (B+C) = 4, (C+A) = 3. Summing efficiencies gives 2*(A+B+C) = 12 => Efficiency of (A+B+C) = 6 units/day. Efficiency of A = (A+B+C) - (B+C) = 6 - 4 = 2 units/day. Time taken by A alone = 60 / 2 = 30 days.
Total work = LCM(12, 15, 20) = 60 units. Efficiency of (A+B) = 5, (B+C) = 4, (C+A) = 3. Summing efficiencies gives 2*(A+B+C) = 12 => Efficiency of (A+B+C) = 6 units/day. Efficiency of A = (A+B+C) - (B+C) = 6 - 4 = 2 units/day. Time taken by A alone = 60 / 2 = 30 days.
This question belongs to:
Maths
Time and Work
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