Question

Question: 1 of 10 Two pipes R and S can fill a tank in 28 and 35 minutes respectively. Both the pipes are opened together, after how many minutes should pipe R be turned off so that the cistern is filled in 20 minutes?​

Answer 1

Answer:

13 minutes

Step-by-step explanation:

1 of 10 Two pipes R and S can fill a tank in 28 and 35 minutes respectively. Both the pipes are opened together, after how many minutes should pipe R be turned off so that the cistern is filled in 20 minutes.

Answer 2

Pipe and Cistern

Given:

Pipe R can fill tank in 28 minutes.

Pipe S can fill tank in 35 minutes.

To find:

After what time the pipe R should be turned off so that the cistern is filled in 20 minutes.

Explanation:

Part filled by R in 1 min = $\frac{1}{28}$

Part filled by S in 1 min = $\frac{1}{35}$

Let R is closed after x min. Then, [Part filled by (R + S) in x min] + [Part filled by S in (20-x) min] = 1

Therefore,

$x(\frac{1}{28} +\frac{1}{35})+(20-x)\times\frac{1}{35} =1$

$\implies x(\frac{9}{140}) +\frac{20-x}{35} =1$

$\implies\frac{9x+80-4x}{140}=1\\\\\implies5x+80=140\\\implies5x=60\\\implies x=12$

Hence, pipe R needs to be closed after 12 minutes to fill the tank in 20 minutes.