Answer

Verified

447.6k+ views

**Hint**: First we will calculate the net tank that is filled in 1 hour and the tank emptied in 1 hour. Hence we will get the net water in the tank after 1 hour. Also we will note that the tank is filled in r hours and hence in 1 hour this net water in the tank will be equal to $ \dfrac{1}{r} $

**:**

__Complete step-by-step answer__Now we are given that a water tap fills a tank in p hours.

Hence in 1 hour $ \dfrac{1}{p} $ part of the tank will be filled.

Also the tap of the bottom of the tank empties it in q hours.

Hence in 1 hour $ \dfrac{1}{q} $ part of the tank will be removed.

Now the water in Tank is water filled in the tank – water removed from the tank.

Hence in 1 hour the total water in the tank will be $ \dfrac{1}{p}-\dfrac{1}{q} $ ………..(1)

Now it is also given that the tank takes r hours to be filled completely.

Hence, in 1 hour $ \dfrac{1}{r} $ tank will be filled. ………….(2)

Hence from equation (1) and equation (2) we get.

$ \dfrac{1}{r}=\dfrac{1}{p}-\dfrac{1}{q} $

**So, the correct answer is “Option B”.**

**Note**: First it is very tempting to select option d as the total water will be water filled – water removed. This problem should be solved step by step as to check the amount of water in a particular time. Also the water that is being removed from the bottom top should be subtracted and not added to the water that is filled in order to get the total water in the tank.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths