MAT Exam 2020 Paper

Concept:When a part of a homogeneous mixture is removed, the same fraction of each component is removed. So, compare water before and after replacement.Explanation:Let the total quantity of the original mixture be $100$ ml.Original water content $= 40\%$ of $100 = 40$ ml.Let $x$ ml of the mixture be replaced.Water removed in $x$ ml of original mixture $= \frac{40x}{100}$ ml.The new mixture added contains $19\%$ water.So, water added in $x$ ml of new mixture $= \frac{19x}{100}$ ml.Final water content becomes $26\%$ of $100$ ml $= 26$ ml.Thus,$40 - \frac{40x}{100} + \frac{19x}{100} = 26$$40 - 26 = \frac{21x}{100}$$14 = \frac{21x}{100}$$x = \frac{1400}{21} = \frac{200}{3}$ mlFraction of mixture replaced $= \frac{x}{100} = \frac{200/3}{100} = \frac{2}{3}$Answer:The quantity of mixture replaced is $\frac{2}{3}$. Hence, the correct option is A.