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. find the number​

Answer 1

Step-by-step explanation:

Let the x be the number at units place and y be the number at digits place no: will be =x+10y

∴ Reverse no: will be 10x+y

Product of digit is 20

xy=20⟶(i)

Now , original number +9=reverse no.

x+10y+9=10x+y

9x−9y=9

x−y=1⟶(ii)

Using formula (x+y)

2

=(x−y)

2

+4xy

(x+y)

2

=1+4(20)

x+y=

81

x+y=9⟶(iii)

Solve (ii) & (iii) ,

x−y=1

x+y=9

2x=10 ⇒x=5

Putting value of x in (ii) ,

5−y=1

y=4

∴ no: is =x+10y

=5+40

=45.