CAPF AC 2021 Q52: General Mental Ability – Quantitative Aptitude
- (a) ₹9,000
- (b) ₹10,000
- (c) ₹15,000
- (d) ₹12,000
Answer: (b) ₹10,000
Explanation
Income, expenditure and savings
Given: incomes of A and B are in the ratio 7 : 10, expenditures in the ratio 2 : 3, and each saves ₹1,000 per month; find B's income.
How to think: income minus expenditure is saving.
Write one equation for A and one for B.
| Step | Working |
|---|---|
| Let | Incomes = 7x and 10x; expenditures = 2y and 3y |
| A saves 1,000 | 7x − 2y = 1,000 |
| B saves 1,000 | 10x − 3y = 1,000 |
| Multiply the first by 3, the second by 2 | 21x − 6y = 3,000 and 20x − 6y = 2,000 |
| Subtract | x = 1,000 |
| B's income | 10x = ₹10,000 |
Check: A earns 7,000 and spends 6,000; B earns 10,000 and spends 9,000.
Expenditure ratio is 6,000 : 9,000 = 2 : 3.
Both save 1,000.
Answer: (b) ₹10,000.
Why each option is right or wrong
- (a) Incorrect. ₹9,000 is B's expenditure, not income.
- (b) CORRECT. x = 1,000, so B's income is 10x = ₹10,000.
- (c) Incorrect. ₹15,000 is not a multiple that fits both ratios with a saving of ₹1,000.
- (d) Incorrect. With ₹12,000, A would earn ₹8,400 and the expenditure ratio would not be 2 : 3.
Key point
Income − expenditure = saving. With income ratio a : b, expenditure ratio c : d and equal saving S: set up ax − cy = S and bx − dy = S, then solve.
Remember
Two ratios, equal savings: two equations, subtract.
Common mistakes
- Giving B's expenditure (₹9,000) when the question asks for income.
- Using the same variable for the income and expenditure ratios.
- Assuming the savings are also in a ratio, when both save the same amount.
Exam tip
Educated guess: B's income is 10 parts, so it should be a clean multiple of 10 that also gives A a clean 7 parts. Test ₹10,000: A gets ₹7,000, spends ₹6,000, B spends ₹9,000, ratio 2 : 3. It works.
Sources
- NCERT Class X Mathematics — Pair of Linear Equations in Two Variables (income and expenditure example)
- NCERT Class VIII Mathematics — Comparing Quantities