Pipes filling and emptying a tank
Question
A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills 3/8th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set X are closed and only half of the pipes of set Y are open, and all pipes of the set (Z) are open, then how long will it take to fill 50% of the tank?
Options
8 minutes
10 minutes
12 minutes
16 minutes
Explanation
First, calculate the time it takes for each entire set to complete 100% of the work: Set X: 70\% in 14 min \rightarrow 100\% in 20 min. Rate = +1/20 per min. Set Y: 3/8 in 6 min \rightarrow 100\% in 16 min. Rate = +1/16 per min. Set Z: 1/2 in 20 min \rightarrow 100\% in 40 min. Rate = -1/40 per min.
Now, adjust the rates based on the fraction of pipes operating: Half of X is open: Rate = (1/2) × (1/20) = 1/40. Half of Y is open: Rate = (1/2) × (1/16) = 1/32. All of Z is open: Rate = -1/40.
Net combined rate = 1/40 + 1/32 - 1/40 = 1/32 per min. To fill 50\% (1/2) of the tank at this rate: Time = (1/2) \div (1/32) = 16 minutes.
Answer: (d).
Question details
Year
2025
Paper
CSAT
Question
Q65
Section
Numerical Ability
Sub-topic
Time & Work
Type
Arithmetic word problem
Difficulty
Hard
Source hint
Pipes-cisterns application
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