CAT 2020 Slot 1 QA Question & Solution
ArithmeticMedium
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
Options
62
55
59
66
Solution
Let $x$ be the strength of group G.
From the information given, $0.65x$ are literate people, and the remaining $0.35x$ are illiterate.
Of the literates, 75% are old people:
$$
0.75 \cdot 0.65x = 0.4875x \quad \text{old literates}
$$
The total number of old people in group G is $0.72x$ (72% of the total).
Hence, the number of old people who are illiterate is:
$$
0.72x - 0.4875x = 0.2325x
$$
The fraction of illiterates who are old is:
$$
\frac{0.2325x}{0.35x} \times 100 \approx 66%
$$
Hence, Option D is the correct answer.