Question

If the number obtained by interchanging the digits of a 2 digits number is 9 more than the original number and the sum of the digits 9,then what is the original number?

Answer 1

Answer:

26 is your answer

Step-by-step explanation:

10y + x = 10x + y +36

9y - 9x = 36

y - x = 4

y + x = 8 ( given)

Therefore 2y = 12 and y = 6 and x = 2

Therefore the original number is 26

Check: 62 - 26 = 36

Answer 2

Answer:

45

$\rule{300}{1}$

Step-by-step explanation:

Let the digits be x and y respectively

So, we are given x + y = 9

Now, a two digit number is of the form of 10a + b, where a and b are the digits. Hence, the two digit number of x and y digits will be 10x + y

Interchanging the digits, we get 10y + x

Given, the number obtained by interchanging is 9 more than the original number. Hence, we have

10y + x = 10x + y + 9

⇒ 10y + x - 10x - y = 9

⇒9y - 9x = 9

⇒9(y - x) = 9

⇒ y - x = 9/9

⇒ y - x = 1

We already had x + y = 9

So, adding the two equations, we get

y - x + x + y = 1 + 9

⇒ 2y = 10

⇒ y = 5

Now put the value of y in any equation to get the value of x

y - x = 1

⇒ 5 - x =1

⇒ x = 5 - 1

⇒ x = 4

So, the digit is 10x + y

⇒10(4) + 5 =

⇒ 45

$\rule{300}{1}$