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SSC Selection Post 2020 PYQ — Question 59

SSC Selection Post - Matriculation Level - 9 Nov 2020 - Shift 3 • Quantitative Aptitude • Q59

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Pipes A and B can fill a tank in 30 minutes and 37121\over2minutes, respectively. C is an outlet pipe. When all the three pipes are opened together, then the tank is full in 25 minutes. In how much time (in minutes) can C alone empty 252\over5th part of the tank?
 

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 20.

The capacity of the tank = 1 unit

A’s rate = 130\frac{1}{30} tank/min

B’s rate =  1752=275\frac{1}{\frac{75}{2}} = \frac{2}{75} tank/min

C’s rate be  - 1x\frac{1}{x} tank/min (since it empties)

Together, all three fill the tank in 25 minutes:

130+275−1x=125\frac{1}{30} + \frac{2}{75} - \frac{1}{x} = \frac{1}{25}

5150+4150−1x=6150⇒9150−1x=6150\frac{5}{150} + \frac{4}{150} - \frac{1}{x} = \frac{6}{150} \Rightarrow \frac{9}{150} - \frac{1}{x} = \frac{6}{150}

⇒1x=9−6150=3150=150⇒x=50\Rightarrow \frac{1}{x} = \frac{9 - 6}{150} = \frac{3}{150} = \frac{1}{50} \Rightarrow x = 50

C alone can empty the full tank in 50 minutes

Time  =25×50 \frac{2}{5} \times 50 = 20  minutes