CAT 2024 Slot 1 · Quant · Question 1

Let the apples and mangoes be 5k and 2k,

so the oranges number 187-7k.

After the sales, the unsold apples are 5k-75 and the unsold oranges are \frac{187-7k}{2}.

The unsold apples to unsold oranges are in the ratio 3:2,

so 2\left( 5k-75 \right)=3\times \frac{187-7k}{2}.

Multiplying through by 2, 4\left( 5k-75 \right)=3\left( 187-7k \right), that is 20k-300=561-21k.

So 41k=861 and k=21.

The original counts are 105 apples, 42 mangoes and 187-147=40 oranges.

The unsold fruits are 105-75=30 apples, 42-26=16 mangoes and \frac{40}{2}=20 oranges.

The total unsold is 30+16+20=66.

Shortcut. The oranges need no separate symbol — writing them as 187-7k keeps the whole question in one unknown, so a single equation finishes it.