Question

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

Please give easy and line by line explanation.

Answer 1

Answer:

the number is 35

Step-by-step explanation:

Let one digit of the number be x , then its ten digits digits will be (8−x) .

So , given number =10(8−x)+x

=80−10x+x

=80−9x

Now if digits are reversed , then Number obtained

=10x+(8−x)

=10x+8−x

=9x+8

According to question

(80−9x)+18=9x+8

98−9x=9x+8

90=18x

x=5

⇒ given number =80−9x

=80−9×5

=80−45

=35

∴ the number is 35

Answer 2

Answer:

Given :-

• A number consists of two digits whose sum is 8. If 18 is added to the number its digits get interchange.

To Find :-

• What is the number.

Solution :-

Let,

➭ Unit's Digit = x

➭ Ten's Digit = 8 - x

Hence, the number will be :

↦ 10(8 - x) + x

↦ 80 - 10x + x

➦ 80 - 9x

◘ Numbers are interchange :

↦ 10x + (8 - x)

↦ 10x + 8 - x

↦ 10x - x + 8

➦ 9x + 8

According to the question,

↦ (80 - 9x) + 18 = 9x + 8

↦ 80 - 9x + 18 = 9x + 8

↦ - 9x - 9x = 8 - 80 - 18

↦ - 18x = - 72 - 18

↦ - 18x = - 90

↦ 18x = 90

↦ x = 90/18

↦ x = 5/1

➠ x = 5

Hence, the required number will be :

⇒ Number = 80 - 9x

⇒ Number = 80 - 9(5)

⇒ Number = 80 - 45

➲ Number = 35

∴ The number is 35.