Question

In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to
1. 59
2. 55
3. 66
4. 62

Answer 1

Correct Answer - Option 3 : 66

Calculation:

Let the total number of people in the group be x

So, the total number of young members = (28/100) × x = 0.28x

Also, the total number of old members = x – 0.28x = 0.72x

It is also given that, 65% of all the members are literates,

Hence, total number of literate people = (65/100) × x = 0.65x

So, the total number of illiterate people = x – 0.65x = 0.35x

Besides, it is also given that 25% of the literates are young.

So, the number of young literates = (25/100) × 0.65x = 0.1625x

Hence, the number of young illiterates = 0.28x – 0.1625x = 0.1175x

Also, we get:

The number of illiterate old people = 0.35x – 0.1175x = 0.2325x

Hence, we can obtain the percentage of old people among the illiterates as:

(0.2325x/0.35x) × 100 = 66.423% ≈ 66%

∴ The percentage of old people among the illiterates is nearly 66% 

It must be remembered here that:

We are asked "the percentage of old people among the illiterates" and not "the percentage of illiterates among the old people"

If the latter was asked, the answer = (0.2325x/0.72x) × 100 = 32.2916 ≈ 32%

This is not the required answer.