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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.

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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?
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APPEARS IN

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