1.

The sum of the digits of a two-digit number is 4 The numbes got by interchangingthe digits is 18 less than the originalnumber what is the number?​

Answer»

Let the Tens DIGIT be x

      the Ones digit be y

We know that Sum of digits is 4

⇒ x + y = 4  ⟶ (Equation 1)

Original number: 10x + y

On interchanging the digits → 10Y + x

According to the question,

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

⇒ 10x + y - 10y - x = 18

⇒ 10x - x + y - 10y = 18

⇒ 9x - 9y = 18

⇒ 9(x - y) = 18

⇒ x - y = 18 ÷ 2

⇒ x - y = 2  ⟶ (Equation 2)

Adding EQUATIONS 1 and 2,

              x + y = 4

      (+)     x - y = 2  

              2x =  6

⇒ x = 3

Now let's Substitute value of x in any one of the equation.

Here I have substituted value of x in Equation 1

x + y = 4

⇒ 3 + y = 4

⇒ y = 4 - 3

⇒ y = 1

For finding the required number,

10x + y

= 10(3) + 1

= 31

Therefore required number is 31


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