# 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

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