Question

An inlet pipe fills up a cistern in 2 hours, while an outlet pipe empties it in 4 hours. The empty cistern was being filled up with both the pipes open for 1 hour, after which someone closed the outlet. How long will it take in total to fill up the cistern?

• A. 2 hours 15 minutes
• B. 2 hours 30 minutes
• C. 3 hours
• D. 1 hour 30 minutes

Answer 1

Answer:

B. 2 hours 30 minutes

Solution:

Given:

Time taken by the inlet to fill the tank = 2 hours.

Time taken by the outlet to empty the tank = 4 hours.

Concept used:

If a pipe fills a tank in t hours, then the quantity of water filled by the pipe in 1 hour = 1 / t

Calculation:

The capacity of the tank filled by the inlet in 1-hour = (1 / 2)

The capacity of the tank emptied by the outlet in 1 hour = (1 / 4)

The capacity of tank filled by inlet and outlet working together in 1 hour

= (1 / 2) + (-1 / 4)

= (2 - 1) / 4

= (1 / 4)

The capacity of tank left to be filled when the outlet was closed

= 1 - (1 / 4)

= 3 / 4.

Time taken by the inlet to fill (3 / 4) of the total capacity of the tank

$=\frac{\frac{3}{4}}{\frac{1}{2}}$

= (3 × 2) / 4

= 1.5 hours.

Total time taken to fill the tank

= 1.5 + 1

= 2.5 hours

= 2 hours and 30 minutes.

∴ The total time taken to fill the tank is 2 hours and 30 minutes.