Question

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39. A cisteen is supplied by three pipes, two of the pipes conveying equal volumes of
water. When one of these two pipes and the third pipe are simultaneously opened, the
cistern is filled in 12 minutes, but when all the three pipes are opened, the cistern is
filled in 7 minutes & 30 seconds. How long does each pipe take separately to fill the
cistern.​

Answer 1

Given:

One of the two pipes ( conveying equal volumes of water) and the third pipe fills the cistern in 12 minutes

All the 3 pipes fills the cistern in 7 minutes 30 seconds i.e., $7\frac{30}{60} = 7\frac{1}{2} = \frac{15}{2}$ minutes

To find:

Time taken by each pipe to fill the cistern separately

Solution:

Let "x" minutes be the time taken by the two pipes conveying equal volumes and "y" minutes be the time taken by the third pipe

So,

In 1 minute, the part of cistern filled by each of the two pipes = $\frac{1}{x}$

In 1 minute, the part of cistern filled by the third pipe = $\frac{1}{y}$

According to the question we can form two equations,

In 1 minute, the part of cistern filled by all the 3 pipes,  

$\frac{1}{x} +\frac{1}{x} +\frac{1}{y} =\frac{2}{15}$ ....... (i)

and

In 1 minute, the part of cistern filled by one of the two pipes and the third pipe,  

$\frac{1}{x} +\frac{1}{y} =\frac{1}{12}$ ....... (ii)

Now, subtracting eq. (ii) from (i), we get

$[\frac{1}{x} +\frac{1}{x} +\frac{1}{y}] - [\frac{1}{x} +\frac{1}{y}] =\frac{2}{15}-\frac{1}{12}$

⇒ $\frac{1}{x} =\frac{8-5}{60}$

⇒ $\frac{1}{x} = \frac{3}{60}$

⇒ $\frac{1}{x} = \frac{1}{20}$

⇒ $x = 20 \:minutes$ ← time taken by each of the two pipes

Substituting the value of x = 20 in eq. (ii), we get

$\frac{1}{20} +\frac{1}{y} =\frac{1}{12}$

⇒ $\frac{1}{y} =\frac{1}{12} - \frac{1}{20}$

⇒ $\frac{1}{y} =\frac{5 - 3}{60}$

⇒ $\frac{1}{y} =\frac{2}{60}$

⇒ $\frac{1}{y} =\frac{1}{30}$

⇒ $y = 30 \:minutes$ ← time taken by the 3rd pipe

Thus, each of the two pipes conveying equal volumes of water takes 20 minutes and the third pipe takes 30 minutes to fill the cistern separately.

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Also View:

Two pipes a and b can fill an empty cistern in 18 and 27 hours respectively. Pipe c can drain the entire cistern in 45 hours when no other pipe is in operation. Initially, when the cistern was empty pipe a and pipe c were turned on. After a few hours pipe a was turned off and pipe b was turned on instantly. In all, it took 55 hours to fill the cistern. For how many hours was pipe b turned on?

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