CAT 2024 Slot 1 QA Question & Solution
Question
A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is
Solution
The number of apples and mangoes are in the ratio 5 : 2.
Let us write the number of apples as 5X and number of mangoes as 2X
This means oranges will be 187-7X.
After selling the remaining fruits,
Apples: 5X-75
Mangoes: 2X-26
Oranges: (187-7X)/2
Unsold Apples to Unsold oranges is 3:2
$\frac{2\left(5x-75\right)}{187-7x}=\frac{3}{2}$
$20x-300=561-21x$
$41x=861$
$x=21$
Total number of unsold fruits will be,
Apples: 30
Mangoes: 16
Oranges: 20
Total is 66.