A vessel is full of mixture of spirit and water in which there is found to be 17% of spirit by measure. Ten litres are drawn off, and the vessel is filled up with water. The proportion of spirit is now found to be \(15\frac{1}{9}\%\) How much does the vessel hold ?
Solution
Correct Answer: Option C
Let the volume of the vessel be v.
Given, 17 % of the vessel is filled with spirit.
∴ volume of spirit present = 17% of v
⇒ volume of spirit present = 0.17v
Now, 10 liters are drawn off, ∴ total volume remaining = v – 10
In 10 liters volume of spirit present = 17% of 10 = 1.7 liters
Thus, volume of spirit remaining = 0.17v – 1.7
As the container is filled with the water again
⇒ % of spirit present now = [(0.17v – 1.7) / (v)] × 100 %
Given in question, % of spirit present in the new situation is 136/9 %
⇒ 136/9 = [(0.17v – 1.7) / (v )] × 100
⇒ 136v = 153v – 1530
⇒ 17v = 1530
⇒ v = 90 litres
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