Question

If the sum of 2-digit number is 5 and when interchanged the number obtained is 9 more than the original number. Find the original number.​

Answer 1

Given :

• The sum of 2-digit number is 5.
• When the number is interchanged, the number obtained is 9 more than the original number.

To Find :

• What is the original number?

Solution :

Let,

☆ Ones digit number be y.

☆ Tens digit number be x.

Then, original number :

⇝ 10x + y

According to the question, we get :

☞ x + y = 5 ⟮Equation no. 1⟯

☞ 10y + x = 10x + y + 9 ⟮Equation no. 2⟯

From equation no. 2, we get :

⇢ 10y - y = 10x - x + 9

⇢ 9y = 9x + 9

⇢ y = 9x + 9/9

Substituting the value of y in equation no. 1 :

↣ x + y = 5

↣ x + 9x + 9/9 = 5

↣ 9x + 9x + 9/9 = 5

↣ 18x + 9/9 = 5

↣ 18x + 9 = 5 × 9

↣ 18x = 45 - 9

↣ x = 36⁄18

↣ x = 2

Now,

Substituting the value of x in equation no. 2 :

⇒ 10y + x = 10x + y + 9

⇒ 10y + 2 = 10(2) + y + 9

⇒ 10y + 2 = 20 + y + 9

⇒ 10y - y = 29 - 2

⇒ 9y = 27

⇒ y = 27⁄9

⇒ y = 3

Therefore, the number is :

⇨ 10x + y

⇨ 10(2) + 3

⇨ 20 + 3

⇨ 23