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SSC Selection Post 2020 PYQ — Question 68

SSC Selection Post - Matriculation Level 2020 - 10 Nov 2020 - Shift 1 • Quantitative Aptitude • Q68

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Pipes X and Y can fill a tank in 30 minutes and 45 minutes, respectively, whereas pipe Z can empty the full tank in 1 hour. Pipes X and Y are opened together for 10 minutes. Then, pipe X is closed, Z is opened instantly and Y continued to fill. The total time (from the beginning) taken to fill the tank is:
 

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 90 minutes.

 

Pipe X fills the tank in 30 minutes → rate =130 \frac{1}{30}  per minute

Pipe Y fills the tank in 45 minutes → rate = 145 \frac{1}{45}  per minute

Pipe Z empties the tank in 60 minutes → rate =  −160- \frac{1}{60} per minute

Combined filling rate =
130+145=3+290=590=118\frac{1}{30} + \frac{1}{45} = \frac{3 + 2}{90} = \frac{5}{90} = \frac{1}{18}

So, water filled in first 10 minutes:
10×118=1018=5910 × \frac{1}{18} = \frac{10}{18} = \frac{5}{9} of tank

Net rate = 145−160=4−3180=1180\frac{1}{45} - \frac{1}{60} = \frac{4 - 3}{180} = \frac{1}{180} per minute

Remaining work = 1−59=491 - \frac{5}{9} = \frac{4}{9} of tank
Time to fill this = 49÷1180=49×180=80\frac{4}{9} ÷ \frac{1}{180} = \frac{4}{9} × 180 = 80 minutes

First part: 10 minutes

Second part: 80 minutes
Total time = 90 minutes