Question

A two-digit number is such that the product of its digits is 12. When 36 is added to this

number, the digits interchange their places. Find the number.

Answer 1

let the ten's digit be 'x' and one's digit be 'y'
The no. is ( 10x + y )
When digits are interchanged the no. becomes ( 10y + x )

ATQ
xy = 12. eq.1
( 10x + y ) + 36 = ( 10y + x )
10x + y + 36 = 10y + x
9x + 36 = 9y
9y - 9x = 36
y - x = 4
y = x + 4. eq.2
Putting value in eq.1
x ( x + 4 ) = 12
x^2 + 4x - 12 = 0

Solve the equation and put them in the required expressions , u will get the answer.