Question

A two-digit number is such that the product of its digits is 35.If 18 is added to the number,the digits interchange their places.Find the number.

Answer 1

Let the two digit number be 10x+ y.
According to the question, x $\times$ y= 35..........(1)
Also, 10x + y +18= 10 y + x
9x - 9y +18= 0
y-x = 2..........(.2)
y= 2+x
Putting the value of x in eq 1, we get
( 2+x ). x = 35
x² + 2x = 35
x² +2x-35=0
( x-5) (x+7). = 0
x=5 , x = -7
Discarding the negative root, x= 5
so, y= 2+5=7
Therefore the two digit number is 10(5)+7 = 57