CAT 2022 Slot 1 · Quant · Question 13

Let the males number 5x and the females 4x.

Let the literate males be 2a and the literate females 3a, matching the ratio 2:3.

Let the illiterate males be 4b and the illiterate females 3b, matching the ratio 4:3.

All males are either literate or illiterate, so 2a+4b=5x.

All females likewise, so 3a+3b=4x.

Multiply the first equation by 3 and the second by 4 to match the b terms: 6a+12b=15x and 12a+12b=16x.

Subtracting the first from the second, 6a=x.

So a=\frac{x}{6}.

The literate males number 2a=\frac{x}{3}, and this is given as 3600.

So x=10800.

The total number of females is 4x=4\times 10800=43200.

Shortcut. Three separate ratios need three separate multipliers — reusing one letter across them is the usual slip. Once the two population equations are written, eliminating b gives x=6a in a single subtraction.