If 3 men or 4 women can plow a field in 43 days, how long will 7 men and 5 women take to plow it? MCQ with Answer and Explanation
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Question #1
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A, B and C can complete a piece of work in 10, 12 and 15 days respectively. They started together but A left 2 days after the start and B left 3 days before the completion of the work. How long did the work last?
Correct Answer: Option A
Explanation:
Total work = LCM(10, 12, 15) = 60 units. Efficiency of A = 6, B = 5, C = 4. Let total days be x. A works for 2 days. B works for (x - 3) days. C works for x days. Total work = 2*6 + (x - 3)*5 + 4*x = 60 => 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 total days be x. A works for 2 days. B works for (x - 3) days. C works for x days. Total work = 2*6 + (x - 3)*5 + 4*x = 60 => 12 + 5x - 15 + 4x = 60 => 9x - 3 = 60 => 9x = 63 => x = 7 days.
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Maths
Time and Work
Question #2
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A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start together but C leaves 4 days before the completion of the work. In how many days was the work completed?
Correct Answer: Option B
Explanation:
Total work = LCM(24, 30, 40) = 120 units. Efficiency of A = 5, B = 4, C = 3. Let the total number of days be x. A and B work for x days, while C works for (x - 4) days. 5x + 4x + 3(x - 4) = 120 => 12x - 12 = 120 => 12x = 132 => x = 11 days.
Total work = LCM(24, 30, 40) = 120 units. Efficiency of A = 5, B = 4, C = 3. Let the total number of days be x. A and B work for x days, while C works for (x - 4) days. 5x + 4x + 3(x - 4) = 120 => 12x - 12 = 120 => 12x = 132 => x = 11 days.
This question belongs to:
Maths
Time and Work
Question #3
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A can complete a work in 8 days and B in 13 days. If they work together, the work will be completed in:
Correct Answer: Option C
Explanation:
Combined rate = 1/8 + 1/13. Required time = 4.95 days.
Combined rate = 1/8 + 1/13. Required time = 4.95 days.
This question belongs to:
Maths
Time and Work
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