The incomes of two people are in the ratio 4 : 3 and their expenses in the ratio 3 : 2. If each saves ₹6,000 a month, what are their incomes?
SHORT ANSWER
₹24,000 and ₹18,000. With incomes 4x, 3x and expenses 3y, 2y: 4x - 3y = 6,000 and 3x - 2y = 6,000. Solving gives x = 6,000 and y = 6,000.
Explain it simply
There are two separate ratios, so you need two separate multipliers: x for income and y for expenses. Savings are income minus expenses, and both people save the same amount, which gives you two equations. Solve them like any pair of simultaneous equations.
Example
Question: Incomes 4 : 3, expenses 3 : 2, each saves ₹6,000. Find the incomes.
- Incomes 4x and 3x, expenses 3y and 2y.
- 4x - 3y = 6,000 ... (1) 3x - 2y = 6,000 ... (2)
- Multiply (1) by 2: 8x - 6y = 12,000. Multiply (2) by 3: 9x - 6y = 18,000.
- Subtract: x = 6,000. Then from (2): 18,000 - 2y = 6,000, so y = 6,000.
- Incomes = 4 x 6,000 = ₹24,000 and 3 x 6,000 = ₹18,000.
Check: expenses are 18,000 and 12,000 (ratio 3 : 2), and both save 6,000.
js
const x = 6000, y = 6000;
console.log([4 * x - 3 * y, 3 * x - 2 * y]); // Output: [6000,6000]What to say in the interview
"I use x for the income ratio and y for the expense ratio, because they are independent. Equal savings give two equations, which solve to x = y = 6,000. Incomes are 24,000 and 18,000."
Common mistakes
- Using the same multiplier for both ratios.
- Stopping at x and reporting 6,000 as an income.