Question

Product of digits of a two digit number is 21.if we add 36 to the number,the new number obtained is a number formed by interchange of the digits.find the number

Answer 1

let the no. be 10x+y
xy = 21
10x+y+36 = 10y+x
9x-9y = -36
x - y = -4
x = y - 4
(y - 4)y = 21
y^2-4y-21 = 0
y^2-7y+3y-21 = 0
y(y-7)+3(y-7) = 0
(y-7)(y+3)=0
y = 7 OR -3
-3 is rejected
x = 3
no. is 37