A can do a piece of work in 10 days B can do it in 15 days With the assistance of they completed the...........

Quantitative Aptitude (CPO) Time and work

A can do a piece of work in 10 days. B can do it in 15 days. With the assistance of they completed the work in 5 days. Find in

how many days C alone can do it?

This questions was previously asked in

SSC CPO 9th Nov 2022 Shift 3

Let’s break this down:

- A’s rate: Can finish the job in 10 days. So in one day, A does 1/10 of the work.

- B’s rate: Does it in 15 days. B does 1/15 of the work daily.

- Together with C: All three finish in 5 days ? (A+B+C) does 1/5 of the work per day.

- Add A and B’s rates: 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 per day.

- So, (A+B+C) = 1/5 per day, and (A+B) = 1/6 per day.

- C’s rate must be (A+B+C) – (A+B) = 1/5 – 1/6 = (6-5)/30 = 1/30 per day.

- So, C alone would take 30 days to finish the work.

Option 3: 30 days is correct.

Here’s a quick word on the options:

- Option 1 (20): That would mean C is much faster than A and B—not matching the math.

- Option 2 (25): Doesn’t fit the rates when you add them up.

- Option 3 (30): The math checks out. C is a solid, steady worker.

- Option 4 (35): Would make C too slow.

Nice work—spot on!

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