Question

Question :-

A number consists of two digits whose sum is 8. If 18 is added to the number its digits are reversed. Find the number.

note :- spam and copied answer get deleted​

Answer 1

$\huge\fbox\red{Answer}$

Given :-

Sum of 2-digit number = 8

If 18 is added to the number, the digits change their places.

To Find :-

The Number

Solution :-

Let one of the number be x

And the other number be 8 - x

According to the question

⇒ 10x + (8 - x) + 18 = 10(8 - x) + x

⇒ 10x + 8 - x + 18 = 80 -10x + x

⇒ 9x + 26 = 80 - 9x

⇒ 9x + 9x = 80 - 26

⇒ 18x = 54

⇒ x = 54/18

⇒ x = 3

One Number = x = 3

Other number = 8 - x = 8 - 3 = 5

Hence, the number is 35.

Answer 2

solution:-

let one's digit be x.

since the sum of the digit is 8.

therefore , ten's digit = 8 - x.

∴ number = 10× (8-x)+x = 80-10x+x = 80 -9x

now,

number obtained by reversing the digit

= 10 × x + ( 8 - x ) = 10x + 8 - x = 9x + 8.

it is given that if 18 is added to the number its digits are reversed.

∴ number + 18 = number obtained by reversing the digits

⇒ 80 - 9x + 18 = 9x + 8

⇒ 98 -9x = 9x + 8

⇒ 98 - 8 = 9x + 9x

⇒ 90 = 18 x

⇒ 18x/18 = 90/18

⇒ x = 5

putting the value of x in (I) , we get

number = 80 - 9 × 5 = 80 - 45 = 35