#### Question

A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.

#### Solution

Let the tens digit be x

Then, the units digit = 12/x

`therefore " Number" =10x+12/x`

And, number obtained by interchanging the Digits `= 10xx12/x+x=120/x+x`

`rArr10x+12/x+36=120/x+x`

`rArr9x+(12-120)/x+36=0`

⇒ 9x^{2} - 108 + 36x = 0

⇒ 9(x^{2} + 4x - 12) = 0

⇒ x^{2} + 6x - 2x - 12 = 0

⇒ x(x + 6) - 2(x + 6) = 0

⇒ (x - 2)(x + 6) = 0

∴ x = 2 or x = -6

But, a digit can never be negative, x = 2

Hence, the digit `=10x+12/x=10(2)+12/2=20+6=26`

Is there an error in this question or solution?

#### APPEARS IN

Solution A Two Digits Number is Such that the Product of the Digits is 12. When 36 is Added to the Number, the Digits Inter Change Their Places Determine the Number. Concept: Solutions of Quadratic Equations by Factorization.