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. 40 days
B. 30 days
C. 20 days
D. 60 days
Answer: Option B
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 11 days and B can complete the same work in 16 days. If they work together, in how many days will the work be completed?
A. 12.52
B. 10.52
C. 8.52
D. 6.52

Correct Answer: Option D


Explanation:
Combined rate = 1/11 + 1/16. Time = 1 ÷ combined rate = 6.52 days.

This question belongs to: Maths Time and Work
Question #2
If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same work?
A. 5 days
B. 4 days
C. 3 days
D. 2 days

Correct Answer: Option C


Explanation:
3 Men = 6 Women => 1 Man = 2 Women. 12 Men + 8 Women = 12(2 Women) + 8 Women = 32 Women. If 6 women do it in 16 days, then 32 women do it in (6 * 16) / 32 = 3 days.

This question belongs to: Maths Time and Work
Question #3
A can do a piece of work in 25 days and B can finish it in 20 days. They work together for 5 days and then A leaves. In how many days will B finish the remaining work?
A. 11 days
B. 9 days
C. 12 days
D. 10 days

Correct Answer: Option A


Explanation:
Total work = LCM(25, 20) = 100 units. Efficiency of A = 4, B = 5. Combined efficiency = 9 units/day. In 5 days, work done = 5 * 9 = 45 units. Remaining work = 100 - 45 = 55 units. Time taken by B to complete remaining work = 55 / 5 = 11 days.

This question belongs to: Maths Time and Work