Question

a 2 digit is such that the product of its digits is 20.if 9 is added to the number the digits interchange their places find the number. with all the steps

Answer 1

Answer is 45

4 * 5 = 20

45+ 9 = 54

Answer 2

Let the digit at unit place = x
and digit at tens place = y
then number(N) is = x + 10y
The new number after interchanging the place of digits = 10x + y
A/Q,
             x.y =  20  ----------------------(1)
Now,    
            (x + 10y) +9 = 10x +y
     or,    10x - x + y - 10y = 9
     or,     9(x-y) =9
     or,       x-y = 1    -----------------(2)
We know that,
(x+y)² + (x-y)²  = 4xy
(x+y)²  =4xy + (x-y)²
or,    (x+y)² = 4×20 + 1²                {from eqn 1}
or,    x+y =√81 = 9     -----------(3)
on adding eqns (1) and (3)
   (x-y) + (x+y) = 1 +9
2x = 10
x = 5
from eqn(1)
y = x-1
when x = 5 ,y = 5-1 = 4       
therefore number is x +10y
         N = 5 + 10×4 = 5 +40 =45