| Pipes P and Q can fill a tank in 10 and 12 h, respectively and C can empty it in 6 h. If all the three are opened at 7 am, at what time will one-fourth of the tank be filled? [SSC (CPO) 2011] |
A) 10 am
B) 10 pm
C) 11 pm
D) 11 am
Correct Answer: B
Solution :
| Given, tank filled by P = 10 h |
| Filled by Q = 12 h and emptied by C = 6 h |
| Part of tank filled in 1 h when all three pipes as opened |
| \[=\frac{1}{10}+\frac{1}{12}-\frac{1}{6}=\frac{6+5-10}{60}=\frac{1}{60}\] |
| Hence, the tank will be filled in 60 h. |
| \[\therefore \]One-fourth of the tank will be filled in \[=\frac{60}{4}=15h\] |
| i.e. the tank will be filled at 10 pm. |
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