Averages , Ratio and Proportion Question 1 - CAT 2022
In a village, the ratio of the number of males to females is 5 : 4. The ratio of the 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:
Step-by-Step Explanation
- Find the number of literate females:
The ratio of literate males to literate females is 2 : 3. Given that there are 3600 literate males:
Literate Females = (3600/2) × 3 = 5400
- Set up the linear system for total populations:
Let the total number of males be 5y and the total number of females be 4y.
Illiterate Males = 5y − 3600
Illiterate Females = 4y − 5400
- Solve using the illiterate ratio constraint:
The ratio of illiterate males to illiterate females is 4 : 3.
(5y − 3600)/(4y − 5400) = 4/3
3(5y − 3600) = 4(4y − 5400)
15y − 10800 = 16y − 21600
y = 10800
Total Females = 4y = 4 × 10800 = 43200
Correct Answer: 43200
💡 FundaMakers Tip:
When given independent row and column ratios (Total vs. Component Breakdown), use the components to form standard expressions. Subtracting the absolute values of the known component (literates) leaves you with a simple cross-multiplication setup that solves the structural variable y instantly.