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## Practice Test Discussion

Q)

A tank can be filled by a pipe A in 2 h and pipe B in 6 h. At 10 am pipe A was opened. At what time will the tank be filled if pipe B is opened at 11 am?

[SSC CGL 2012]

• Explanation

According to the question,

Pipe A fills the tank in 2 hours (in 1 hour it fills $\frac{1}{2}$ part of the tank)

Pipe B fills the tank in 6 hours (in 1 hour it fills $\frac{1}{6}$ part of the tank)

As pipe A was opened at 10:00 am and it worked alone till 11:00 am. In 1 hour it will fill $\frac{1}{2}$ part of the tank.

the remaining $\frac{1}{2}$ part of the tank will be filled by both Pipe A and B.

According to the formula, if pipe A can comletely fill a tank in x hours and pipe B can comletely fill a tank in y hours, then the time taken by both pipes together to fill the tank is $\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}}$ hours.

So,  (both the pipes together will fill $\frac{3}{2}$ part of the tank)

So, Time taken by both pipes to fill $\frac{3}{2}$ part of the tank = 60 minutes
Time taken to fill $\frac{1}{2}$ part = $\frac{60×3}{2}×\frac{1}{2}$ = 45 minutes

Therefore, the tank will be filled at 11:45 AM

Hence option C is correct.

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