Question

The product of the digits of a two digit numbers is 12. If 36 is added to the number, a number is obtained which is the same the number obtained by reversing the digits of the original number. Find the original number.

Answer 1

Answer:

26

Step-by-step explanation:

Let digits be x and y.

xy = 12

10x + y + 36 = 10y + x

36 = 9y-9x

9(4) = 9(y-x)

4 = y-x

4+x=y

Substituting value of y in xy=12,

x(4+x)=12

x²+4x=12

x²+4x-12=0

(x+6)(x-2) = 0

Therefore x = -6 or 2,

but a number cannot have a negative digit,

therefore x = 2.

xy=12 ⇒ 2y = 12 ⇒ y =6

10x + y = 20 + 6 = 26

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