S1 and S2 can do a piece of work together in 18 days S2 and S3 can do the same work together in 27 d...........

Quantitative Aptitude (MTS) Time and work

S1 and S2 can do a piece of work together in 18 days,S2 and S3 can do the same work together in 27 days, while S3 and S1

can do it together in 54 days. In how many days can all 3, working together, do 50% of the work?

8 days

6 days

7 days

9 days

- Let's assume the total work is 1 unit.

- S1 and S2 together can complete 1/18 of the work per day.

- S2 and S3 together can complete 1/27 of the work per day.

- S3 and S1 together can complete 1/54 of the work per day.

- By solving these equations:

- S1 + S2 = 1/18

- S2 + S3 = 1/27

- S3 + S1 = 1/54

- Add all three equations:

- 2(S1 + S2 + S3) = 1/18 + 1/27 + 1/54

- 2(S1 + S2 + S3) = 1/9

- S1 + S2 + S3 = 1/18

- Therefore, all three together can complete 1/18 of the work per day. To complete 50% (0.5) of the work:

- Days = 0.5 / (1/18) = 9 days

- Correct Option: Option 4 - 9 Days

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