Question

The sum of the digits of a two-digit number is 8. If the number formed by reversing the digits is less than the original number by 18, find the original number as well as reversed number​

Answer 1

Step-by-step explanation:

Given :

• The sum of two digits of a number is 8.
• If we reverse the digits the difference between them is 18.

To find :

➡ The numbers.

Solution :

Let's assume :

The numbers are x as tens digit and y as ones digit.

Thier sum is 8

So,

➡ x + y = 8.......(i)

The number formed :

➡ 10x + y

Reversing the digits we get :

➡ 10y + x

According to the question :

$\sf : \implies \: (10x + y) - (10y + x) = 18 \\ \sf : \implies \: 10x + y - 10y - x = 18 \\ \sf : \implies \: 9x - 9y = 18 \\ \sf : \implies \: 9(x - y) = 18 \\ \sf : \implies \: x - y = \frac{18}{9} \\ \sf : \implies \: x - y = 2......(ii)$

Subtracting both the equation :

$\bf \: x + y = 8 \\ { \bf{ \underline{x - y = 2}}} \\ \sf : \implies \: 2x = 6 \\ \sf : \implies \: x = \frac{6}{2} \\ \sf : \implies \: x = 3$

After solving we get :

➡ x = 3

Substituting the value of x in the equation (i) :

➡ x + y = 8

➡ 3 + y = 8

➡ y = 8 - 3

➡ y = 5 ans.

Therefore,

The number is :

➡ 10x + y

➡ 10(3) + 5

➡ 30 + 5

➡ 35 or, 53 ans.