Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes, respectively. Pipe R draws the water out from the storage tank at a rate of 34 litres per minute. P, Q and R operate at a constant rate.
If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?
26.8
60.0
120.0
127.5
ANSWER
The capacity of the storage tank is 120 litres, option (C).
Official answer: CSource: Official answer key, GATE 2022 IN (IIT Kharagpur)
Let the capacity be litres. A pipe that fills the tank in minutes works at litres per minute, so P fills at and Q at .
Rates of pipes working together add, so the combined filling rate is
R drains at . Since the tank empties, the outflow is larger than the inflow, and the net draining rate is .
Time = volume / net rate, and one hour is :
Solve: , so and .
Check: P and Q together fill at , so the net drain is , and , which is one hour. The answer is (C).
KEY IDEA
Turn each pipe into a rate in litres per minute. A pipe that fills a tank of litres in minutes pours in litres per minute. Rates add, drains count as negative, and the time to empty is capacity divided by the net outflow. Here that gives one linear equation in .
WATCH OUT FOR
Setting the inflow equal to the outflow, , gives , which is option (D). At that capacity the tank's level never changes, so it would never empty. The one-hour emptying time needs a net outflow of litres per minute, so the equation is . A second slip is adding the fill times () instead of the rates ().
From the GATE 2022 IN paper. Every question of this paper · Download the full paper · All 58 Numerical questions, with notes
