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

Let the two-digit number be 10x + y, where x = tens digit, y = units digit.

Step 1: Product condition

x × y = 12 … (1)

Step 2: Interchange condition

If digits interchange, new number = 10y + x

Given: (10x + y) + 36 = (10y + x)

⇒ 9x – 9y = –36

⇒ x – y = –4 … (2)

Step 3: Solve equations

From (2): x = y – 4

Put in (1): (y – 4) × y = 12

⇒ y² – 4y – 12 = 0

⇒ (y – 6)(y + 2) = 0

⇒ y = 6 (since digit can’t be –2)

Then x = y – 4 = 2

Number = 10x + y = 10×2 + 6 = 26

✅ Final Answer: The number is 26.