Question

Two pipes can fill a cistern in 12 and 15 minutes respectively.Both are opened together , but at the end of 3 minutes the first is turned off.How much longer will the cistern take to/fill?

Answer 1

Answer:

Time taken to fill the cistern 11.25 minutes

Step-by-step explanation:

Let pipe $a$ can fill empty cistern in 12 minutes

Thus, pipe $a$ can empty parts of cistern 1 minute $=\frac{1}{12}$

Let pipe $b$ can fill empty cistern in 15 minutes

Thus, pipe $b$ can empty parts of cistern 1 minute $=\frac{1}{15}$

Total parts of cistern is LCM of 12 and 15 $=60\hspace{0.1cm}parts$

Pipe $a$ can fill parts of cistern in 1 minute $=\frac{60}{12}=5\hspace{0.1cm}parts$

Pipe $b$ can fill parts of cistern in 1 minute $=\frac{60}{15}=4\hspace{0.1cm}parts$

Given that both pipes are opened together and pipe $a$ is closed after 3 minutes

This means, for first 3 minutes, both pipe $(\,a + b)\,$ fills the cistern.

Parts of cistern filled by pipe $(\,a + b)\,$ in 1 minute $= 5 + 4 = 9\hspace{0.1cm}parts$

Parts of cistern filled by pipe $(\,a + b)\,$ in 3 minutes $= 3 \times 9 = 27\hspace{0.1cm}parts$

Parts of cistern remaining $=60 - 27 = 33\hspace{0.1cm}parts$

33 parts of cistern are filled by pipe $b$ only

Pipe $b$ can fill parts of cistern in 1 minute $= 4\hspace{0.1cm}parts$

Thus, 4 parts of cistern filled by pipe $b$ in 1 minute

33 parts of cistern filled by pipe $b$ in $\frac{33}{4} = 8.25$ minutes

Time taken to fill the cistern $=3 + 8.25 = 11.25\hspace{0.1cm}minutes$