CAT 2023 Slot 3 · Quant · Question 9

Work with sugar fractions, since that is all the question tracks.

In mixture A the ratio is 3:2, so sugar is \frac{2}{5}, that is 40%.

In mixture B the ratio is 7:3, so sugar is \frac{3}{10}, that is 30%.

Mixture C combines A and B in the ratio 2:3, so take 2 units of A and 3 units of B, making 5 units in all.

The sugar from A is 2\times \frac{2}{5}=\frac{4}{5}.

The sugar from B is 3\times \frac{3}{10}=\frac{9}{10}.

The total sugar is \frac{4}{5}+\frac{9}{10}=\frac{8+9}{10}=\frac{17}{10}.

So the sugar fraction in C is \frac{17/10}{5}=\frac{17}{50}, that is 34%.

Adding an equal amount of milk doubles the volume while adding no sugar.

So the sugar fraction halves to \frac{17}{100}, that is 17% — the fourth option.

Shortcut. Sugar percentages mix by weighted average, so C is \frac{2\times 40+3\times 30}{5}=34\% in one line. Equal milk then halves it, and halving 34 gives 17 — with no need to track cocoa or coffee at all.