Question: 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?
Options:
A) 10 am
B) 10 pm
C) 11 pm
D) 11 am
Show Answer
Answer:
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.