Mathematics — Standard (041) — CBSE Class 10 board question

Let the incomes of the two persons be ₹9x and ₹7x, and their expenditures be ₹4y and ₹3y respectively.

Since each saves ₹5,000:

$$9x - 4y = 5000 \quad \text{...(1)}$$
$$7x - 3y = 5000 \quad \text{...(2)}$$

Solving by Elimination:

Multiply (1) by 3 and (2) by 4:

$$27x - 12y = 15000 \quad \text{...(3)}$$
$$28x - 12y = 20000 \quad \text{...(4)}$$

Subtract (3) from (4):

$$x = 5000$$

Substitute in (1): $9(5000) - 4y = 5000 \Rightarrow y = 10000$

Monthly incomes:

• Person 1: $9x = 9 × 5000 =$ ₹45,000
• Person 2: $7x = 7 × 5000 =$ ₹35,000

Source: Chapter 3, Section 3.3.2 (Elimination Method)

The question has two parts — forming equations and solving them — so both must be shown clearly. The incomes are expressed as $9x$ and $7x$ (not separately), which keeps the ratio 9:7 built in. Saving = Income − Expenditure, giving two equations. Use the elimination method to score full method marks; show each step. The examiner checks: correct equations (1 mark), correct method (1 mark), correct final incomes (1 mark).