# A Two-digit Number is 3 More than 4 Times the Sum of Its Digits. If 8 is Added to the Number, the Digits Are Reversed. Find the Number. - Mathematics

Definition

A two-digit number is 3 more than 4 times the sum of its digits. If 8 is added to the number, the digits are reversed. 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  10y + x.

The number is 3 more than 4 times the sum of the two digits. Thus, we have

 10 y + x = 4(x +y)+ 3

 ⇒ 10 y + x = 4x + 4y + 3

 ⇒ 4x + 4y -10y -x =-3

 ⇒ 3x - 6y = -3

 ⇒ 3 ( x - 2 y)= -3

 ⇒ x - 2y = -3/3

 ⇒ x - 2y = -1

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

If 18 is added to the number, the digits are reversed. Thus, we have

 ( 10 y + x )+ 18 = 10x + y

 ⇒ 10x + y -10y -x =18

 ⇒ 9x -9y = 18

 ⇒ 9( x - y)=18

 ⇒ x -y = 18 /9

 ⇒ x - y =2

So, we have the systems of equations

 x - 2y =-1

 x - y =2

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

Subtracting the first equation from the second, we have

 ( x - y)-(x - 2y )=2 -(-1)

 ⇒ x - y -x + 2y =3

 ⇒ y = 3

Substituting the value of in the first equation, we have

 x - 2xx3 =-1

⇒ x - 6 = -1

 ⇒ x = -1+6

 ⇒ x = 5

Hence, the number is  10 xx3 + 5 = 35

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.7 | Q 9 | Page 86