#### Question

The product of the digits of a two digit number is 24. If its unit’s digit exceeds twice its ten’s digit by 2; find the number.

#### Solution

Let the ten’s and unit’s digit of the required number be x and y respectively.

From the given information,

x x y = 24

y = 24/x .....(1)

Also y = 2x + 2 [Using (1)]

`24/x = 2x^2 + 2x`

`2x^2 + 2x - 24 = 0`

`x^2 + x - 12 = 0`

(x + 4)(x - 3) = 0

x = -4,3

The digit of a number cannot be negative so x = 3

∴ y= 24/3 = 8

Thus the required number is 38

Is there an error in this question or solution?

Solution The Product of the Digits of a Two Digit Number is 24. If Its Unit’S Digit Exceeds Twice Its Ten’S Digit by 2; Find the Number. Concept: Quadratic Equations.