Question: A tank can be filled by pipe A in 2 h and pipe B in 6 h. At 10 am pipe A was opened. At what time will tank be filled if pipe B is opened at 11 am?
Options:
A) 12: 45 am
B) 5 pm
C) 11: 48 am
D) 12 pm
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, tank filled by A in 2h and tank filled by B in 6 h.
Then, part of the tank filled in 1 h by pipe A $ =\frac{1}{2} $
Part of the tank filled in 1 h by pipe B $ =\frac{1}{6} $
According to the question,
Pipe A was opened at 10 am and till, 11 am, pipe A alone worked. So, part of the tank filed between 10 am to 11 am by pipe A $ =\frac{1}{2} $
$ \therefore $ Remaining work $ =1-\frac{1}{2}=\frac{1}{2} $
Now, remaining work will be done by both pipes
(A + B).
Tank filled by (A + B) working together
$ =\frac{xy}{x+y} $ [where, $ x=2, $ $ y=6 $ ]
$ =\frac{2\times 6}{6+2}=\frac{12}{8}=\frac{3}{2}h $
Hence, half tank filled by (A + B)
$ =\frac{3}{2\times 2}h=\frac{3}{4}h=\frac{3}{4}\times 60=45\min $
Hence, the tank will be filled at 11: 45 am.
BETA
