CAT 2025 Slot 2 · Quant · Question 13

Let Lakshmi spend 2k and Meenakshi spend 3k.

Lakshmi's income to Meenakshi's expenditure is 6:7, so Lakshmi's income is \frac{6}{7}\times 3k=\frac{18k}{7}.

Lakshmi's saving is income minus expenditure: \frac{18k}{7}-2k=\frac{4k}{7}.

Savings are in the ratio 4:9, so Meenakshi's saving is \frac{9k}{7}.

Meenakshi's income is expenditure plus saving: 3k+\frac{9k}{7}=\frac{30k}{7}.

The ratio of incomes is \frac{18k}{7}:\frac{30k}{7}=18:30=3:5.

Shortcut. Lakshmi's saving came out as exactly \frac{4k}{7} — matching the 4 in the savings ratio. So read the savings directly as \frac{4k}{7} and \frac{9k}{7}, and the incomes are 2k+\frac{4k}{7} and 3k+\frac{9k}{7}, i.e. \frac{18k}{7} and \frac{30k}{7}. Choosing the expenditures as 2k and 3k is what makes the sevenths cancel so cleanly.