IPMAT Question Paper 2021 | IPM Indore Quantitative Ability

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Question 5 : There are two taps, T₁ and T₂, at the bottom of a water tank, either or both of which may be opened to empty the water tank, each at a constant rate. If T₁ is opened keeping T₁ closed, the water tank (initially full) becomes empty in half an hour. If both T₁ and T₂ are kept open, the water tank (initially full) becomes empty in 20 minutes. Then, the time (in minutes) it takes for the water tank (initially full) to become empty if T₂ is opened while T₁ is closed is

Video Explanation

Explanatory Answer

The tank has two taps T₁ and T₂.
It is given that the Tap T₁ empties the tank in 30 minutes and also that the taps T₁ and T₂ together can empty the tank in 20 minutes.
So, understanding this in terms of ‘1 minute’.
Tap T₁ will empty \(\frac{1}{30} t h\) of the tank in 1 minute
And T₁ and T₂ will together empty \(\frac{1}{20} t h\) of the tank in 1 minute
In this 1 minute, Out of the \(\frac{1}{20} t h\) tank empties by the two taps together, T₁ empties \(\frac{1}{30} t h\) of the tank and the rest is emptied by T₂.
So, to find out the portion of the tank emptied by T₂ in 1 minute we can simply subtract T₁ from the total.
Which is, \(\frac{1}{20}\) - \(\frac{1}{30}\) 
= \(\frac{1}{60}\)
So T₂ empties \(\frac{1}{60}\)th of the tank in 1 minute, and so to empty the entire tank it will require 60 minutes.

The answer is '60'

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