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Percentage of old people among illiterates

CAT 2020 Slot 1 · Quantitative Ability · Easy · Percentages

This is an easy Quantitative Ability question from the CAT 2020 Slot 1 paper. It tests Percentages. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

  1. A.

    59

  2. B.

    62

  3. C.

    66

  4. D.

    55

Answer

C

Explanation

Assume total population =100= 100.

  • Young =28= 28, Old =72= 72.
  • Literate =65= 65, Illiterate =35= 35.

Young Literates =25% of 65=16.25= 25\% \text{ of } 65 = 16.25. Young Illiterates =28−16.25=11.75= 28 - 16.25 = 11.75.

Old Illiterates =Total Illiterates−Young Illiterates=35−11.75=23.25= \text{Total Illiterates} - \text{Young Illiterates} = 35 - 11.75 = 23.25.

Percentage of old people among illiterates: =23.2535×100%≈66.42%≈66%= \frac{23.25}{35} \times 100\% \approx 66.42\% \approx 66\%

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