Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-35

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?                                                                             [SSC (CGL) 2013]

A) 12: 45 am

B) 5 pm

C) 11: 48 am

D) 12 pm

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.