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