CAT 2020 Set-1 | Question: 70

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 

• A.  $62$
• B.  $55$
• C.  $66$
• D.  $59$

Answer 1

Let the total number of people in the group be $100.$

• The number of people who are young $ = 28 \% \; \text{of} \; 100 = \frac{28}{100} \times 100 = 28$
• The number of people who are old $ = 100 – 28 = 72$

Among $100$ people, $65$ are literate, then $35$ people should be illiterate.

The number of literate people who are young $ = 25 \% \; \text{of} \; 65  = \frac{25}{100} \times 65 = 16.25$

• The number of literate people who are old $ = 65 – 16.25 = 48.75$
• The number of illiterate people who are old $ = 72 – 48.75 = 23.25$

$\therefore$ The percentage of old people among the illiterates $ = \left(\frac{23.25}{35} \right) \times 100\% = 66.42 \% \simeq 66\%.$

Correct Answer $: \text{C}$