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

Let the two numbers be $x$ and $y$, where $x > y$.

$$x + y = 105 \quad \text{...(1)}$$
$$x - y = 45 \quad \text{...(2)}$$

Adding (1) and (2):
$$2x = 150 \implies x = 75$$

Substituting in (1):
$$75 + y = 105 \implies y = 30$$

∴ The two numbers are 75 and 30.

• This is a standard elimination method problem (Chapter 3). Form two equations from the given conditions, then add them to eliminate $y$ and find $x$, then substitute back.
• Examiners award 1 mark for correct equation formation and 1 mark for correct solution. Always verify: 75 + 30 = 105 ✓ and 75 − 30 = 45 ✓.