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CAT 2020 Slot 1 — QA Question 6

PercentageEasy

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

Answer & solution

  • A

    55

  • 66

  • C

    59

  • D

    62

Solution

Easy

Build a 2×2 table of Young/Old against Literate/Illiterate using a convenient base of 100 members. Fill the literate column from the given percentages, get the rest by subtraction, then read off the old fraction within the illiterate column.

1

Fix the totals (base 100). Young =28=28, Old =72=72; Literate =65=65, Illiterate =35=35.

young literates=25% of 65=16.25old literates=65−16.25=48.75\begin{aligned} &\text{young literates}=25\%\text{ of }65=16.25\\ &\text{old literates}=65-16.25=48.75 \end{aligned}
2

Get the illiterate column by subtraction. Subtract the literate counts from the row totals.

young illiterates=28−16.25=11.75old illiterates=72−48.75=23.25\begin{aligned} &\text{young illiterates}=28-16.25=11.75\\ &\text{old illiterates}=72-48.75=23.25 \end{aligned}

The table (out of 100 people):

LiterateIlliterateTotal
Young16.2511.7528
Old48.7523.2572
Total6535100
3

Compute the old share among illiterates.

old illiteratesall illiterates×100=23.2535×100≈66.4%\begin{aligned} &\frac{\text{old illiterates}}{\text{all illiterates}}\times 100=\frac{23.25}{35}\times 100\approx 66.4\% \end{aligned}
≈66%\approx 66\%
CAT 2020 Slot 1 QA Q6: In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates — Solution | TheCATExam