Question

A 2digit no.is such that product of digit is 12. When 36 is added to the no. the digits interchanged. Find the no.

Answer 1

let the numbers be a and b where a is in ten's digit.

so the number is =10a+b

a*b=12 --eq1

10a+b+36=10b+a

36=9b-9a

4=b-a --eq2

from eq1 a=12/b

using the above result in eq2

4=b-(12/b)

4b=b^2-12 or b^2-4b-12=0

on solving the quadratic equation

b=-2 or b=6

therefore a=-6 or a=2

hence the numbers are -62 or 26