Capacity of a tank

A tank is two thirds full. After drawing off 100 litres of water , it is just one quarter full. what is the capacity of the tank

Solution

Let x be the capacity of the tank or the amount of water when the tank is full.

Here is how to solve this problem:

Amount of water in the tank now - 100 = amount of water left after removing 100


Since the tank is 2/3 full, the amount of water in the tank now is 2/3 times x

or 2x/3


Amount of water left after removing 100 is 1/4 times x or x/4


We them get this equation

2x/3 - 100 = x/4


2x/3 -100 + 100 = x/4 + 100


2x/3 = x/4 + 100


2x/3 - x/4 = x/4 - x/4 + 100


2x/3 - x/4 = 100


(2x × 4) / (3 × 4) - (x × 3) / (4 × 3) = 100


8x/12 - 3x/12 = 100


(8x - 3x) / 12 = 100


5x / 12 = 100


Multiply both sides by 12


(5x × 12) / 12 = 100 × 12


5x = 1200


Divide both sides by 5


5x/5 = 1200/5


x = 240

the capacity of the tank is 240 liters.


Indeed, 2/3 of 240 = (2 × 240)/ 3 = 480 / 3 = 160

160 - 100 = 60

And 60 is 1/4 of 240