NIMCET 2025 — Reasoning PYQ

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Question

NIMCET 2025 — Reasoning PYQ

NIMCET | Reasoning | 2025

A two digit number is such that the product of its digits is 12. If 36 is added to the mumber, the digits interchange their places. What is the mumber?

Choose the correct answer:

Explanation

1. Let the Number be Represented:

Let tens digit be $x$ and units digit be $y$ .

\text{Original Number} = 10x + y

\text{Interchanged Number} = 10y + x

2. Formulating Equations:

Product: $x \cdot y = 12$
Difference: $(10y + x) - (10x + y) = 36$

$9y - 9x = 36$

$y - x = 4 \implies y = x + 4$

3. Solving for $x$ :

Substitute $y$ in the product equation:

x(x + 4) = 12

x^2 + 4x - 12 = 0

(x + 6)(x - 2) = 0

x = 2 \text{ (Since digit cannot be negative)}

4. Finding $y$ and the Number:

y = 2 + 4 = 6

\text{Number} = 10(2) + 6 = 26

Correct Option: (A)