| If two pipes function together, the tank will be filled in 12 h. One pipe fills the tank in 10 h faster than the other. How many hours does the faster pipe take to fill up the tank? |
A) 20
B) 60
C) 15
D) 25
Correct Answer: A
Solution :
| Let one pipe takes m h to fill the tank. |
| Then, the other pipe takes \[(m-10)h.\] |
| According to the question, |
| \[\therefore \] \[\frac{1}{m}+\frac{1}{(m-10)}=\frac{1}{12}\] |
| \[\Rightarrow \] \[\frac{m-10+m}{m\,\,(m-10)}=\frac{1}{12}\] |
| \[\Rightarrow \]\[12\,\,(m-10+m)=m\,\,(m-10)\] |
| \[\Rightarrow \]\[{{m}^{2}}-34m+120=0\] |
| \[\Rightarrow \]\[{{m}^{2}}-30\,\,m-4\,\,m+120=0\] |
| \[\Rightarrow \] \[(m-30)(m-4)=0\] |
| \[\therefore \] \[m=30\]or 4 |
| \[\therefore \]Faster pipe will take \[(30-10)\,\,h=20\,\,h\] to fill the tank. |
You need to login to perform this action.
You will be redirected in
3 sec
