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# 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. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### 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

⇒ 9x2 - 108 + 36x = 0

⇒ 9(x2 + 4x - 12) = 0

⇒ x2 + 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.
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