Averages , Ratio and Proportion Question 3 - CAT 2025
The ratio of expenditures of Lakshmi and Meenakshi is 2 : 3, and the ratio of income of Lakshmi to expenditure of Meenakshi is 6 : 7. If the excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is 4 : 9, then the ratio of their incomes is:
Step-by-Step Explanation
- Set up the variables systematically based on ratios:
Let Lakshmi's expenditure be Eₗ and Meenakshi's expenditure be Eₘ.
Given Eₗ/Eₘ = 2/3, choose Eₗ = 2x and Eₘ = 3x.
The ratio of Lakshmi's income (Iₗ) to Meenakshi's expenditure (Eₘ) is given as 6 : 7:
Iₗ/Eₘ = 6/7
Iₗ/3x = 6/7
Iₗ = 18x/7
- Determine savings allocations:
Lakshmi's Savings (Sₗ) = Iₗ − Eₗ
= 18x/7 − 2x
= 4x/7
Given the savings ratio Sₗ/Sₘ = 4/9:
(4x/7)/Sₘ = 4/9
⟹ Sₘ = 9x/7
- Find the income of Meenakshi and the final ratio:
Meenakshi's Income (Iₘ) = Eₘ + Sₘ
= 3x + 9x/7
= 30x/7
Ratio of Incomes (Iₗ : Iₘ)
= 18x/7 : 30x/7
= 18 : 30
= 3 : 5
Correct Option: A
💡 FundaMakers Tip:
When multiple cross-cutting ratios share common parameters (like expenditure linking both metrics here), anchor the variables around that shared metric. Expressing all equations in terms of the base element x keeps your work unified and lets the scaling denominators cancel out naturally in the final step.