Alekh and Alia can together do a piece of work in 5 days which Alia and Aman together can do in 15 d...........

Quantitative Aptitude (RBI Grade B) Time and work

Alekh and Alia can together do a piece of work in 5 days which Alia and Aman together can do in 15 days. After Alekh has been working at it for 4 days and Alia for 5 days, Aman then takes up and completes the work alone in 4 days. In how many days can Alia do the work alone?

30 days

45 days

50 days

25 days

None of these

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Explanation:

Let the work done by Alekh, Alia and Aman in 1 day be x. y and z respectively (Alekh’s 4 days + Alia’s 5 days + Aman’s 4 days) work = 1
(Alekh + Alia) 4 days + (Alia + Aman) 1 day + Aman 3 days work = 1….. (1)

From question: Work done by Alekh and Alia in 1 day = 1/5 Work done by Alia and Aman in 1 day = 1/15

In equation (1) 1/5 × 4 + 1/15 × 1 + 3z = 1

4/5 + 1/15 + 3z = 1

12/15 + 1/15 + 3z = 1

13/15 + 3z = 1

3z = 1-13/15 3z = 2/15

z = 2/45

Aman can do work in 5 days

y + z = 1/15

y + 2/45 = 1/15

y = 1/15 – 2/45

y = 3/45 – 2/45