Question

Pipes X and Y can fill a tank in 30 minutes and 45 minutes, respectively, whereas pipe Z can empty the full tank in 1 hour. Pipes X and Y are opened together for 10 minutes. Then, pipe X is closed, Z is opened instantly and Y continued to fill. The total time (from the beginning) taken to fill the tank is:
1. 80 minutes
2. 100 minutes
3. 75 minutes
4. 90 minutes

Answer 1

Correct Answer - Option 4 : 90 minutes

Given:

Time taken by pipe X to fill the tank = 30 minutes

Time taken by pipe Y to fill the tank = 45 minutes

Time taken by pipe Z to empty the tank = 60 minutes

Working time of (X + Y) = 10 minutes

Concept:

Consider the total work to be 1 unit. Take the sign of Z as negative because it empties the tank.

Formula used:

1 unit work = 1/(Total time taken to complete the work)

Calculation:

(X + Y)'s 1 min work = (1/30) + (1/45)

= (3 + 2)/90

= 5/90

∴ Unit of work done by (X + Y) in 10 min = (10 × 5)/90

= 50/90

Unit of work left = 1 - (50/90)

= (90 - 50)/90

= 40/90

This work will be done by Y and Z together.

(Y - Z)'s 1 min work = (1/45) - (1/60)

= (4 - 3)/180

= 1/180

∴ Time taken by (Y and Z) to complete the whole work = 180 min

∴ Time taken by (Y and Z) to complete 40/90 unit of work = 180 × (40/90)

= 80 minutes.

∴ Total time taken to finish the whole work = (Time taken by X + Y) + (Time taken by Y and Z)

= 10 min + 80 min

= 90 min