# A Number Consist of Two Digits Whose Sum is Five. When the Digits Are Reversed, the Number Becomes Greater by Nine. Find the Number. - Mathematics

Definition

A number consist of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.

#### Solution

Let the digits at units and tens place of the given number be x and y respectively. Thus, the number is 10 y + x.

The sum of the digits of the number is 5. Thus, we have  x + y = 5

After interchanging the digits, the number becomes 10 x + y.

The number obtained by interchanging the digits is greater by 9 from the original number. Thus, we have

10 x + y = 10 y + x + 9

⇒ 10 x + y - 10y - x =9

 ⇒ 9x -9 y = 9

⇒ 9 ( x - y)= 9

 ⇒ x - y = 9/9

 ⇒ x - y = 1

Here x and y are unknowns. We have to solve the above equations for x and y.

Adding the two equations, we have

( x + y) + ( x - y) = 5 + 1

⇒  x + y + x - y = 6

 ⇒ 2x = 6

 ⇒ x = 6/2

 ⇒ x = 3

Substituting the value of in the first equation, we have

 3 + y = 5

⇒ y = 5-3

 ⇒ y = 2

Hence, the number is  10 xx2 + 3 = 23

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.7 | Q 3 | Page 86