Question

A jar full of spirit contains 40% alcohol. A part of this spirit is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The fraction of spirit replaced is:

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{2}{5}$
• D. $\frac{3}{5}$

Answer 1

The correct option is B

$\frac{2}{3}$

Let initial quantity of spirit be 100 litres.
Quantity of Alcohol=40 litres
Let x litre of this spirit is replaced by x litre of spirit containing 19% alcohol.
Quantity of alcohol in new spirit = 40 - 40% of x + 19% of x
$=40l-\frac{40x}{100}l+\frac{19x}{100}=40l-\frac{21x}{100}l$
According to question,
$40l-\frac{21x}{100}l=26l\frac{21x}{100}=14x=\frac{14\times 100}{21}=\frac{2}{3}\times 100$
Quantity of spirit replaced, $\frac{x}{100}=\frac{2}{3}$
So, correct option is (c).