A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. If A, B and C work together, in how many days will they complete the work? MCQ with Answer and Explanation

A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. If A, B and C work together, in how many days will they complete the work?
A. 8 days
B. 12 days
C. 10 days
D. 5 days
Answer: Option C
Solution (By JKExamLibrary)
Total work = LCM(12, 15, 20) = 60 units. Efficiency of (A+B) = 5, (B+C) = 4, (C+A) = 3. Sum of efficiencies = 2 * (A+B+C) = 12 => Efficiency of (A+B+C) = 6 units/day. Time taken together = 60 / 6 = 10 days.

This question belongs to: Maths Time and Work

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Practice More Time and Work Questions

Question #1 Report Error
A can complete a work in 19 days and B can complete the same work in 24 days. If they work together, in how many days will the work be completed?
A. 14.6
B. 10.6
C. 12.6
D. 16.6

Correct Answer: Option B


Explanation:
Combined rate = 1/19 + 1/24. Time = 1 ÷ combined rate = 10.6 days.

This question belongs to: Maths Time and Work
Question #2 Report Error
9 men can complete a work in 19 days. If 13 men work at the same rate, in how many days will the work be completed?
A. 13.15
B. 15.15
C. 19.15
D. 17.15

Correct Answer: Option A


Explanation:
Total work = 9 × 19 = 171 man-days. Required days = 171/13 = 13.15 days.

This question belongs to: Maths Time and Work
Question #3 Report Error
A and B work together. A alone can complete the work in 24 days and B alone in 26 days. What percentage of the total daily work is contributed by A?
A. 54.5
B. 57.0
C. 52.0
D. 59.5

Correct Answer: Option C


Explanation:
A share = (1/24) / (1/24+1/26) ×100 = 52.0%.

This question belongs to: Maths Time and Work