CAT 2022 Slot 1 QA Question & Solution
Question
In a village, the ratio of number of males to females is 5 : 4. The ratio of number of literate males to literate females is 2 : 3. The ratio of the number of illiterate males to illiterate females is 4 : 3. If 3600 males in the village are literate, then the total number of females in the village is
Solution
In the question, it is given that the ratio of number of literate males to literate females is 2 : 3.
Given, the number of literate males = 3600
The number of literate females = $\frac{3600}{2}\times3$ = 5400
Males : Females = 5 : 4
Let the number of males be 5y and the number of females be 4y
Illiterate males = 5y - 3600
Illiterate females = 4y - 5400
It is given,
$\ \frac{\ 5y-3600}{4y-5400}=\frac{4}{3}$
15y - 10800 = 16y - 21600
y = 10800
Number of females = 4y = 4*10800 = 43200