Question

a two digit number is such that the product of digits is 20 when 9 is added to the number then the digits interchange their places find the number

Answer 1

Let the number be 10b + a where a is the digit at ones place and b is the digit at tens place.

Given that,
ab = 20.........(1)

Also,

10b + a + 9 = 10a + b
=> 9b +9 = 9a
=> b + 1 = a........ (2)

Substituting a = b + 1 in equation (1),

b ( b + 1) = 20

By simple observation, you can tell that b = 4
as 4*5 = 20

Since b = 4, a= b +1 = 5

Hence the original number is 10b + a = 45