Question

a two digit number is such that the product of its digits is 20 if 9 is added to the number the digits interchange their places

Answer 1

Given :Let the x be th number at units place and y be the number at digits place

number will be =x+10y

Reverse number will be 10x+y

Product of digit is 20

Therefore,xy=20 -----{1}

original number + 9=reverse number

x+10y +9=10x +y

9x-9y=9

x-y=1-------{2}

using formula (x+y)²=(x-y)²+4xy

 (x+y)²=(1)²+4(20)   [ by using equation 1 and 2]

 (x+y)²=1+80=81

 (x+y)=9-----(3)

solve equation 3 and 2

x+y=9

x-y=1

_______

by adding, we get,

2x=10 

⇒x=5

y=9-5

y=4

so x and y are 5 and 4

so number is x +10y =5 +10x4=5+40=45

∴Required number is 45