#### Question

In a two-digit number, the ten’s digit is bigger. The product of the digits is 27 and the difference between two digits is 6. Find the number.

#### Solution

Given, the difference between the two digits is 6 and the ten’s digit is bigger than the unit’s digit.

So, let the unit’s digit be x and ten’s digit be (x + 6).

From the given condition, we have:

x(x + 6) = 27

x² + 6x – 27 = 0

x² + 9x – 3x – 27 = 0

x(x + 9) – 3(x + 9) = 0

(x + 9) (x – 3) = 0

x = -9, 3

Since, the digits of a number cannot be negative. So, x = 3.

Unit’s digit = 3

Ten’s digit = 9

Thus, the number is 93.

Is there an error in this question or solution?

Solution In a Two-digit Number, the Ten’S Digit is Bigger. the Product of the Digits is 27 and the Difference Between Two Digits is 6. Find the Number. Concept: Quadratic Equations.