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? MCQ with Answer and Explanation

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?
A. 20 days
B. 60 days
C. 40 days
D. 30 days
Answer: Option D
Solution (By JKSSB Mock Tests)
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.

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Practice More Time and Work Questions

Question #1
A can complete a work in 21 days and B in 31 days. If both work together, in how many days will the work be completed?
A. 20.02
B. 15.02
C. 12.52
D. 17.52

Correct Answer: Option C


Explanation:
Combined rate = 1/21 + 1/31. Time = 12.52 days.

This question belongs to: Maths Time and Work
Question #2
A can do a piece of work in 10 days, B in 15 days. They work together for 2 days and then A leaves. In how many days will B complete the remaining work?
A. 12 days
B. 8 days
C. 10 days
D. 11 days

Correct Answer: Option C


Explanation:
Total work = LCM(10, 15) = 30 units. Efficiency of A = 3, B = 2. Combined efficiency = 5 units/day. In 2 days, work completed = 2 * 5 = 10 units. Remaining work = 30 - 10 = 20 units. Time taken by B to complete remaining work = 20 / 2 = 10 days.

This question belongs to: Maths Time and Work
Question #3
A can complete a work in 9 days and B in 16 days. If they work together, the work will be completed in:
A. 5.76
B. 20.76
C. 15.76
D. 10.76

Correct Answer: Option A


Explanation:
Combined rate = 1/9 + 1/16. Required time = 5.76 days.

This question belongs to: Maths Time and Work