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UPSC Prelims 2025 CSAT, question 45

Topic: Arithmetic

Q45

A set (X)(X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y)(Y) of 10 pipes fills 3/8th3/8^{th} of the tank in 6 minutes. A third set (Z)(Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set XX are closed and only half of the pipes of set YY are open, and all pipes of the set (Z)(Z) are open, then how long will it take to fill 50% of the tank ?

  1. (a) 8 minutes
  2. (b) 10 minutes
  3. (c) 12 minutes
  4. (d) 16 minutesCorrect answer

Solution.

Answer: (d) 16 minutes

  1. Set XX (2020 pipes) fills 70%70\% in 1414 minutes (5%5\% per minute), so half of Set XX (1010 pipes) fills 2.5%2.5\% of the tank per minute.
  2. Set YY (1010 pipes) fills 38=37.5%\frac{3}{8} = 37.5\% in 66 minutes (6.25%6.25\% per minute), so half of Set YY (55 pipes) fills 3.125%3.125\% per minute; all 1616 pipes of Set ZZ empty 50%50\% in 2020 minutes (2.5%2.5\% per minute).
  3. With 1010 pipes of XX, 55 pipes of YY, and all 1616 pipes of ZZ open, the net filling rate is 2.5%+3.125%−2.5%=3.125%2.5\% + 3.125\% - 2.5\% = 3.125\% per minute, so filling 50%50\% of the tank takes 503.125=16\frac{50}{3.125} = 16 minutes.