A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer
Let the tens digit be x and units digit be y.
So the number = 10x + y.
Condition 1: Product of digits = 24
$$xy = 24 \quad \Rightarrow \quad y = \frac{24}{x} \tag{1}$$
Condition 2: When 18 is subtracted, digits interchange.
$$10x + y - 18 = 10y + x$$
$$9x - 9y = 18$$
$$x - y = 2 \tag{2}$$
Substituting (1) in (2):
$$x - \frac{24}{x} = 2$$
$$x^2 - 2x - 24 = 0$$
$$x^2 - 6x + 4x - 24 = 0$$
$$(x-6)(x+4) = 0$$
So x = 6 or x = −4.
Since x is a digit, x = 6, and $y = \dfrac{24}{6} = 4$.
The required number is 64.
Verification: 6 × 4 = 24 ✓; 64 − 18 = 46 (digits interchanged) ✓
Source: Pair of Linear Equations in Two Variables, Chapter 3
---
Explanation
- Examiners award marks at each key step: forming both equations (1 mark), reducing to a quadratic (1 mark), solving and rejecting the negative digit (1 mark), stating the number with verification (1 mark).
- Represent the 2-digit number as 10x + y — this standard form is essential.
- Reject x = −4 explicitly (a digit cannot be negative) to show completeness.
- Always verify both conditions at the end; CBSE often awards the final mark for correct verification.