Question

A boy distributes chocolates among four of his friends in the ratio \(\dfrac{1}{3}:\dfrac{1}{4}:\dfrac{1}{5}:\dfrac{1}{6}\). The minimum number of chocolates this boy should have, in order to do this distribution is
1. 60
2. 114
3. 57
4. 54
5.

Answer 1

Correct Answer - Option 3 : 57

Given:

The ratio of distribution among friends = (1/3) : (1/4) : (1/5) : (1/6)

Concept used:

In order to convert fractional ratio into whole number ratio, multiply each term with LCM of denominators

Calculation:

We first convert the fraction ratio into whole number ratio

Since, LCM of denominators 3, 4, 5, 6 is 60, we multiply the ratio by 60.

On rearranging, the ratio = (60/3) : (60/4) : (60/5) : (60/6) = 20 : 15 : 12 : 10

Considering that chocolate is distributed in whole number, the minimum number of chocolates can be when the common ratio is 1.

⇒ The minimum number of chocolates = 20 + 15 + 12 + 10 = 57

∴ The minimum number of chocolates the boy should have, in order to do this distribution is 57.