Profit and Loss Question 5 - CAT 2020
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:
Step-by-Step Explanation
Assume the total number of people in the group is 100.
- Young members = 28
- Old members = 100 − 28 = 72
- Literate members = 65
- Illiterate members = 100 − 65 = 35
We are given that 25% of the literate group are young:
Young Literates = 25% of 65 = 16.25
Now, calculate the number of old literate individuals:
Old Literates = Total Literates − Young Literates
= 65 − 16.25 = 48.75
To find the number of old illiterate individuals, subtract the old literates from the total old population:
Old Illiterates = Total Old − Old Literates
= 72 − 48.75 = 23.25
The question asks for the percentage of old people specifically within the illiterate cohort:
Percentage = (Old Illiterates / Total Illiterates) × 100
= (23.25 / 35) × 100
≈ 66.43%
The nearest value among the options is 66.
Correct Option: D
💡 FundaMakers Tip:
Complex overlapping demographic groups are easiest to manage using a 2x2 Matrix Grid instead of Venn diagrams. Label rows as Young / Old and columns as Literate / Illiterate. As you calculate each value based on a total sample size of 100, fill in the matrix boxes. The remaining values can then be found through simple subtraction across rows and columns.