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

$59$

$55$

$66$

$62$

✅ Correct Option: 3

Let us assume we have $100$ people in total to make percentage calculations easier.

Given Information:

$28\%$ are young → $28$ people are young

Rest are old → $72$ people are old

$65\%$ are literate → $65$ people are literate

Rest are illiterate → $35$ people are illiterate

$25\%$ of literates are young

Since $25\%$ of the $65$ literates are young:

Young literates $= 25\% \times 65 = 0.25 \times 65 = 16.25$ people

We know:

Total young people $= 28$

Young literates $= 16.25$

Therefore: Young illiterates $= 28 - 16.25 = 11.75$ people

This makes sense because all young people are either literate or illiterate.

Among the $35$ illiterate people:

Young illiterates $= 11.75$

Old illiterates $= 35 - 11.75 = 23.25$ people

Percentage of old people among illiterates:

$\dfrac{\text{Old illiterates}}{\text{Total illiterates}} \times 100= \dfrac{23.25}{35} \times 100 = 66.43\%$

This problem uses overlapping groups where people are classified by age (young vs old) and education (literate vs illiterate). The key is finding the overlap and working backwards to determine all combinations.

Answer: $66.43\%$

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In a group of people, 28%28\%28% of the members are young while the rest are old. If 65%65\%65% of the members are literates, and 25%25\%25% of the literates are young, then the percentage of old people among the illiterates is nearest to

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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