Spirit Problem
Algebra
Level
3
A container is full of spirit. 40 litres of spirit is taken out and the container is filled with water. This process is repeated twice further. Now, the ratio of spirit to water in the container is 27:98. Find the capacity of the container in litres.
The answer is 100.
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1 solution
The ratio 27:98 is the same as 21.6% spirit and 78.4% water.
Water is originally at 100%, and this is reduced to 21.6% after being diluted 3 times. So x^3 = 0.216 which gives x=0.6 i.e each refill is diluting the SPIRIT by 60%.
Considering only the first time we diluted, 40L of WATER dilutes the spirit by 40%, therefore the original volume must be 100L of water.