Question

A two digit number is such that the product of the digits is 12. when 36 is added to the number the digits interchanging their places. find the two digit number.

Answer 1

let the digit in ones place be x

and the digit in tens place be y

therefore, the two digit no. = 10y+x

the reversing no. = 10x+y

A/Q,

xy=12

=>x=12/y

and,

10y+x+36=10x+y

=>10y-y+x-10x = - 36

=>9y - 9x = - 36

=> y - x = - 36/9

=>y -12/y = - 4

=>(ysq. - 12)/y = - 4

=> ysq. - 12 = -4y

=> y sq. +4y -12 = 0

=> y sq. +4y-3y - 12 = 0

=> y(y+4) - 3 (y+4) = 0

=> (y+4)(y-3) = 0

either y= -4(not possible) or y= 3

therefore, y=3,x=12/3= 4

the req. 2 digit no. = 10*3 + 4 = 34