Question: A B and C are three taps connected to a tank. A and B together can fill the tank in $ 6h, $ B and C together can fill it in $ 10h $ and A and C together can fill it in $ 7\frac{1}{2}h. $ In how much time all three would take to fill the tank?
Options:
A) $ 10h $
B) $ 12h $
C) $ 20h $
D) $ 5h $
Show Answer
Answer:
Correct Answer: D
Solution:
- Given, time taken by (A + B) to fill the tank $ =6h $
$ \therefore $ Part of tank filled by (A + B) in $ 1h=\frac{1}{6} $ … (i)
(if a pipe fills a tank in x h, then the part of tank filled in $ 1h=\frac{1}{x} $ )
Similarly, part of tank filled by (B + C) in $ 1h=\frac{1}{10} $ … (ii)
and part of tank filled by (C + A) in $ 1h=\frac{2}{15} $ …(iii)
On adding Eqs. (i), (ii) and (iii), we get
$ A+B+B+C+C+A=\frac{1}{6}+\frac{1}{10}+\frac{2}{15} $
$ \Rightarrow $ $ 2A+2B+2C=\frac{5+3+4}{30} $
$ \Rightarrow $ $ 2(A+B+C)=\frac{12}{30} $
$ \Rightarrow $ $ (A+B+C)=\frac{12}{60} $
$ \Rightarrow $ $ (A+B+C)=\frac{1}{5} $
Hence, A, B and C all three can fill the tank in 5 h.
(if a pipe fills $ \frac{1}{x} $ part of the tank in $ 1h, $ then the time taken by the pipe to fill the full tank $ =xh $ )
BETA
