Question

A two digit number is such that the product of its digits is 12. When 9 is added to the number, the digits interchange their places. The number is ___.

Answer 1

Let the two digit number be ab.

$a\times b=12$

When 9 is added to the number

$10a+b+9=10b+a$

$9a-9b+9=0$

$a-b+1=0$

$a-\frac{12}{a}+1=0$

$a^2+a-12=0$

$(a+4)(a-3)=0$

a = -4 is not accepted. So, a = 3, b = 4

The number is 34 .