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Multiple Choice Questions

A and B can together complete a piece of work in 18 days B and C can together complete the same work...........

Quantitative Aptitude (MTS) Time and work

A and B can together complete a piece of work in 18 days, B and C can together complete the same work in 24 days and A and

C can together complete it in 36 days. In how many days can A, B and C, working together, complete this piece of work?

This questions was previously asked in

SSC MTS 5th July 2022 Shift-3

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Explanation:

- Let's define work rates:
- A and B together complete the work in 18 days.
- B and C together complete the work in 24 days.
- A and C together complete the work in 36 days.

- Calculate combined work rate of A, B, and C:
- A + B = 1/18 of work per day
- B + C = 1/24 of work per day
- A + C = 1/36 of work per day

- Add all equations:
- (A + B) + (B + C) + (A + C) = 1/18 + 1/24 + 1/36

- Simplify to find the rate of 2(A + B + C):
- 2(A + B + C) = (4 + 3 + 2)/72 = 9/72 = 1/8

- Therefore, A, B, and C together can complete the work in half the time:
- A + B + C = 1/16 of work per day

- So, A, B, and C can complete the work together in 16 days.
- ✅ **Option 2 - 16** days is the correct answer.

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