Question

A two digit number such that product of its digit is 14 if 45 is added to the number the digit interchange their places find the numbers.

Answer 1

consider, number is xy.

x * y =14

xy + 45=yx

Number should be 27......

Answer 2

solution :

let the digits be x and y, then both x and y are less than 10 and both are whole numbers. product of digits =14 it means,

x y=14.......(1)

and when 45 is added both are interchanged.

The number was 10x+y and after interchanging it will be 10y+x

it means, 10x+y +45 = 10y+x

=>9x+45=9y

=>x+5=y

put value of y in eq(1)

=>x (x+5)=14

=>x x+5x-14=0

=>x x +7x -2x-14=0

=>x(x+7)-2(x+7) =0

=>(x+7)(x-2)=0

=>x=2 or x=-7(minus is not possible) so x=2

and x=y+5, =>y=7 so number is 27

answer