A pipe can fill a cistern in 20 minutes where as the cistern when full

1.	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 min2. 70 min3. 60 min4. 48 min
Answer» 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

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 min2. 70 min3. 60 min4. 48 min

Answer» 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

Discussion

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