Question

A number consists of two digits whose some is 9. If 9 is added to the number its digits are inter changed. Find the number.

Answer 1

Given :

• A number consists of two digits whose some is 9.

• I9 is added to the number its digits are inter changed.

To find :

• The number =?

Step-by-step explanation :

Let the digits at ones place be x

Then the digits at tens place = 9-x (sum of

two digits is 9)

Therefore the number = 10 (9 - x + x)

= 90 - 10x + x

= 90 - 9x

Now,

Number obtained by reversing the digits = 10x + 9 - x = 9x+9

It is given if 9 is added to the number.,it's digits are interchanged.

➮ 90 - 9 x + 9 = 9x + 9

➮ 99 - 9x = 9x + 9

➮ 99 - 9 = 9x + 9x

➮ 90x = 18 x

➮ x = 90/18

➮ x = 5

Therefore, we get the value of x = 5.

And tens place= 9 - x = 9 - 5 = 4

Thus , the number is 45.

Answer 2

Correct Question :

A number consists of two digits whose sum is 9. If 9 is added to the number its digits are inter changed. Find the number.

Solution :

Let the digit in the units place be y and the digit in the tenth place be x.

Then, the original number is 10x+y.

Sum of the digits = x+y = 9_______Equation 1

Now, according to the question when 9 is added to the number it's digits get interchanged then,

10x + y +9 = 10y + x

10x - x + y - 10y = - 9

9x - 9y = - 1

9(x - y) = - 9

x - y = - 1

y - x = 1_____________Equation 2

From Equation 1 & 2, we conclude

x + y = 9

x = 9 - y

So, y - x = 1

y - (9 - y) = 1

y - 9 + y = 1

2y = 1 + 9 = 10

y = 10/2 = 5.

And, x = 9 - y

x = 9 - 5 = 4.

Therefore, the number is 45.