| Two pipes A and B can fill a tank in 24 and 32 min, respectively. If both the pipes are opened together, after how much time pipe B should be closed, so that the tank is full in 9 min? |
A) 40 min
B) 30 min
C) 10 min
D) 20 min
Correct Answer: D
Solution :
| Part filled by A in 1 min \[=\frac{1}{24}\] |
| Part filled by B in 1 min \[=\frac{1}{32}\] |
| Let B is closed after x min. |
| Then, [part filled by \[(A+B)\] in x min] + [part filled by A in \[(9-x)\]min] = 1 |
| \[\therefore \]\[x\left( \frac{1}{24}+\frac{1}{32} \right)+(9-x)\times \frac{1}{24}=1\] |
| \[\Rightarrow \]\[x\left( \frac{4+3}{96} \right)+\frac{(9-x)}{24}=1\] |
| \[\Rightarrow \]\[\frac{7x}{96}+\frac{(9-x)}{24}=1\]\[\Rightarrow \]\[\frac{7x+4\,\,(9-x)}{96}=1\] |
| \[\Rightarrow \]\[7x+4\,\,(9-x)=96\]\[\Rightarrow \]\[7x+36-4x=96\] |
| \[\Rightarrow \]\[7x-4x=96-36\]\[\Rightarrow \]\[3x=60\]\[\Rightarrow \]\[x=\frac{60}{3}=20\] |
| Hence, B must be closed after 20 min. |
You need to login to perform this action.
You will be redirected in
3 sec
