Two workers A and B are engaged to do a piece of work. Working together they would take 8 hours less than the time taken by A alone, and 4.5 hours less than the time taken by B alone. Find the time they take to complete the work together. MCQ with Answer and Explanation
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Question #1
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A, B and C can do a piece of work in 10, 15 and 30 days respectively. If they work on alternate days in the order A, B, C, in how many days will the work be completed?
Correct Answer: Option B
Explanation:
Total work = LCM(10, 15, 30) = 30 units. Efficiency of A = 3, B = 2, C = 1. In a 3-day cycle (A on day 1, B on day 2, C on day 3), work completed = 3 + 2 + 1 = 6 units. Number of cycles required = 30 / 6 = 5 cycles. Total days = 5 * 3 = 15 days.
Total work = LCM(10, 15, 30) = 30 units. Efficiency of A = 3, B = 2, C = 1. In a 3-day cycle (A on day 1, B on day 2, C on day 3), work completed = 3 + 2 + 1 = 6 units. Number of cycles required = 30 / 6 = 5 cycles. Total days = 5 * 3 = 15 days.
This question belongs to:
Maths
Time and Work
Question #2
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A can complete a work in 14 days and B can complete the same work in 19 days. If they work together, in how many days will the work be completed?
Correct Answer: Option C
Explanation:
Combined rate = 1/14 + 1/19. Time = 1 ÷ combined rate = 8.06 days.
Combined rate = 1/14 + 1/19. Time = 1 ÷ combined rate = 8.06 days.
This question belongs to:
Maths
Time and Work
Question #3
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A can do a work in 13 days and B in 17 days. In how many days will they complete 75% of the work together?
Correct Answer: Option C
Explanation:
Combined time for full work multiplied by 0.75 = 5.52 days.
Combined time for full work multiplied by 0.75 = 5.52 days.
This question belongs to:
Maths
Time and Work
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