CAT 2022 Slot 1 · Quant · Question 3

Take 1 part of the original mixture and 3 parts of pure sugar syrup, making 4 parts in all.

The original mixture is half lemon juice and half sugar syrup.

So the 1 part of mixture contributes \frac{1}{2} of lemon juice and \frac{1}{2} of sugar syrup.

The 3 parts of pure syrup contribute no lemon juice and 3 of sugar syrup.

The new mixture therefore holds \frac{1}{2} of lemon juice.

Its sugar syrup is \frac{1}{2}+3=\frac{7}{2}.

The ratio is \frac{1}{2}:\frac{7}{2}, which is 1:7 — the fourth option.

Shortcut. Only the lemon juice needs tracking: it is \frac{1}{2} of 1 part out of 4 parts total, so lemon juice is \frac{1}{8} of the whole. Everything else is syrup, giving 1:7 at once.