A and B can do a work in 15 days and 25 days respectively They worked together for 5 days after whic...........

Quantitative Aptitude (MTS) Time and work

A and B can do a work in 15 days and 25 days, respectively. They worked together for 5 days, after which B was replaced by C

and the remaining work was completed by A and C in the next 4 days. In how many days will C alone complete the same work?

This questions was previously asked in

SSC MTS 7th October 2021 Shift-1

24 days

20 days

15 days

25 days

- A can complete the work alone in 15 days.

- B can complete the work alone in 25 days.

- A and B together can do the work at the rate of 1/15 + 1/25 = 8/75 of the work per day.

- In 5 days, they complete 5 * (8/75) = 40/75 or 8/15 of the work.

- Therefore, 1 - 8/15 = 7/15 of the work is still remaining.

- A and C together finish the remaining 7/15 of the work in 4 days, meaning their combined rate is (7/15) / 4 = 7/60 of the work per day.

- A alone does 1/15 of the work per day. Therefore, C’s rate is (7/60) - (1/15) = (7/60) - (4/60) = 3/60 or 1/20.

- C alone can complete the work in 20 days.

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