Question

P and Q can complete art and craft in 15 days, Q and S can complete it in 18 days while P and S can complete same art and craft in 24 days. Find the time taken by P, Q and S in completing the art and craft work together.
1. 360/29 days
2. 720/59 days
3. 6 days
4. 180/59 days

Answer 1

Correct Answer - Option 2 : 720/59 days

Given:

P and Q can complete art and craft in 15 days.

Q and S can complete it in 18 days while P and S can complete same art and craft in 24 days.

Concepts used:

Time = Work/Efficiency

1 day work of individual = Work/Time

Calculation:

1 day work of P and Q = 1/15

1 day work of Q and S = 1/18

1 day work of P and S = 1/24

⇒ 1 day work of P, Q and S = ½ × {(1/15) + (1/18) + (1/24)} = 59/720 = 59/720

⇒ Time taken by P, Q and S to complete full art and craft work = 720/59 days 

∴ P, Q and S took 720/59 days to complete full art and craft work.