Question

A fruit vendor has 36 bananas, 42 apples, 30 oranges and 24 guavas. The fruit vendor decides to make identical fruit baskets with the same number of bananas, apples, oranges and guavas in each basket. The minimum number of apples in each basket is .

Answer 1

To have minimum number of apples in each basket, maximum number of fruit baskets need to be made.

To find the maximum number of identical fruit baskets, with atleast 1 banana, 1 apple, 1 orange and 1 guava in each basket. we need to evaluate GCD of the 4 numbers.

The factor trees of $36,42,30$ and $24$ are as follows:

$\to 36=2\times 2\times 3\times 3$
$\to 42=2\times 3\times 7$
$\to 30=2\times 3\times 5$
$\to 24=2\times 2\times 2\times 3$

The common factors among these are $2$ and $3.$
$\therefore$ GCD is $2\times 3=6.$

Hence, the maximum number of fruit baskets is $6.$

There are total $42$ apples.
$\therefore$ Minimum number of apples in each fruit basket $=\frac{\text{Total number of apples}}{\text{Number of fruit baskets}}$
$=\frac{42}{6}=7\text{apples}$.