Question

A pipe can fill a cistern in 20 minutes where as the cistern when full can be emptied by a leak in 28 minutes. When both are opened, The time taken to fill the cistern is:
1. 80 min
2. 70 min
3. 60 min
4. 48 min

Answer 1

Correct Answer - Option 2 : 70 min

Given:

Pipe one can fill tank in 20 minutes

Pipe two can empty tank in 28 minutes

Formula Used:

\(\frac{1}{{{\rm{work\;of\;A\;and\;B}}}} = \frac{1}{{\;work\;of\;A}} + \frac{1}{{\;work\;of\;B}}\)

Calculation:

Let the Minutes taken by A and B working together be x

\(\frac{1}{{{\rm{work\;of\;A\;and\;B}}}} = \frac{1}{{\;20}} - \frac{1}{{\;28}}\) (we take work of pipe 2 as negative because it empties the tank)

⇒ 1/x = (7 - 5)/140 = 2/140 = 1/70

⇒ x = 70 Minutes

∴ The Time taken to fill the cistern is 70 Minutes