Question

A tap can fill a cistern in 5 hours and another can empty it in 20 hours. If both the taps are opened simultaneously, how much time it will take to fill the tank?

a) 6 hrs
b) 16/3 hrs
c) 7 hrs
d) 20/3 hrs

Answer 1

Answer:

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Answer 2

It takes 20/3 hours to fill the tank. Hence Option D is correct

Solution:

According to question there are two taps  

Let them to be ‘A’ and  ‘B’

Tap A can fill the cistern in 5 hours

Tap B can empty the cistern in 20 Hours

So, if we take LCM (5, 20) = 20

So, let us assume the capacity of cistern be 20

$\text { Efficiency of } \mathrm{A}=\frac{\text { Total Capacity of cistern }}{\text { Time taken By A }}=\frac{20}{5}=4$

$\text { Similarly, efficiency of } \mathrm{B}=\frac{\text { Total Capacity of cistern }}{\text { Time taken By } B}=\frac{20}{20}=1$

So, when both taps are open simultaneously the  

net efficiency = efficiency of A – efficiency of B

net efficiency = 4 – 1 = 3

$\text { Total time in filling the tank }=\frac{\text { Total Capacity of cistern }}{\text { Net efficiency }}=\frac{20}{3}$

Hence it takes 20/3 hours to fill the tank. Hence Option D is correct

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