Incomes, expenditures and equal savings — Aptitude Question
Incomes, expenditures and equal savings: The incomes of two people are in the ratio 3 : 4 and their expenditures in… Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 150 seconds
Question
The incomes of two people are in the ratio 3 : 4 and their expenditures in the ratio 5 : 7. If each saves ₹200, what is the income of the first?
Options
- ₹800
- ₹1,000
- ₹1,200
- ₹1,500
Show the answer and the worked solution
Correct answer: C. ₹1,200
Worked solution
- 3x − 5y = 200 and 4x − 7y = 200.
- Multiply: 12x − 20y = 800 and 12x − 21y = 600.
- Subtracting gives y = 200, so 3x = 200 + 1,000 = 1,200.
- The first income is 3x = ₹1,200.
Answer: ₹1,200.
The idea
Two ratios need two variables. Income − expenditure = savings gives one equation per person, and eliminating one variable finishes it. This is the standard two-ratio problem of the chapter.
Shortcut. Back-substitute: an income of ₹1,200 makes the second ₹1,600; taking off ₹200 savings leaves expenditures of ₹1,000 and ₹1,400, exactly 5 : 7.
Common trap. "₹1,000" — solving y = 200 and taking 5y, the first person's expenditure, instead of the income 3x.