Question

Two pipes A and B can fill a reservoir in 18 and 24 minutes respectively. Both pipes are opened together but 3 minutes before the reservoir is full, pipe A is closed. How much time will the reservoir take to fill?

please answer!!!​

Answer 1

Both pipes are opened together but 3 minutes before the reservoir is full, pipe A is closed, then the reservoir take to fill in 12 minutes.

Step-by-step explanation:

Pipe A can fill a reservoir = 18 minutes  

So, In 1 minute, part filled by pipe A = $\frac{1}{18}$

Pipe B can fill a reservoir = 24 minutes

So, in 1 minute, part filled by pipe B = $\frac{1}{24}$

∴ In 1 minute, part of the reservoir filled by pipe A & B together is,

= $\frac{1}{18} + \frac{1}{24}$

= $\frac{4+3}{72}$

= $\frac{7}{72}$

It is given that, firstly both the pipes are opened then 3 minutes before the reservoir is full, pipe A is closed i.e., pipe B fills the reservoir for the last 3 minutes before the reservoir is completely filled.

So, part of the reservoir filled by pipe B in 3 minutes = 3 * $\frac{1}{24} = \frac{1}{8}$

∴ Unfilled part of the reservoir = 1 – $\frac{1}{8} = \frac{7}{8}$ ← This $\frac{7}{8}$th part of the reservoir is filled by both the pipes A and B.

Therefore,

If $\frac{7}{72}$th  part is filled in 1 minute

Then the $\frac{7}{8}$th part will be filled by both pipe A & B in = $\frac{72}{7} * \frac{7}{8}$ = 9 minutes

Thus,  

The reservoir will be completely filled in,

= 9 + 3

= 12 minutes

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