Question

the sum of two digit of a two digit number is 11 if 9 is added to the number its digits are reversed find the number

Answer 1

Let’s Suppose first digit is x and second digit is y
so, the two digit number is: 10x + y
sum of digits: x + y = 11
if digits are reversed then the new number: 10y + x
new number is 9 less than original number: (10x + y) - (10y + x) = 9

So, ultimately we got two equations to solve:
1. x + y = 11
2. (10x + y) - (10y + x) = 9

Now, let’s solve equation 2,
(10x + y) - (10y + x) = 9
=> 10x + y - 10y - x = 9
=> 9x - 9y = 9
=> 9 ( x - y ) = 9
=> x - y = 9/9
=> x - y = 1
=> x = 1 + y

Let’s put this value of x in equation (1),
x + y = 11
=> 1 + y + y = 11
=> 2y + 1 = 11
=> 2y = 11 - 1
=> y = 10/2
=> y = 5

Now, let’s put y = 5 in equation (1),
x + y = 11
=> x + 5 = 11
=> x = 11 - 5
=> x = 6

So, the original number is: 10x + y = 10*6 + 5 = 65

Ans: 65