Question

22. A number consists of two digits, whose sum is 8. If 18 is added to the number, its digits are interchanged. Find
the number.
(1) 53
(2135
(3) 92
(4) 63​

Answer 1

The answer is 35
3+5=8
35+18=53(which is interchanged)

Answer 2

Answer :-

• That number is 35.

Given :-

• A number consists of two digits, whose sum is 8. If 18 is added to the number, it's digits are changed.

To Find :-

• That number.

Solution :-

Let

• Ones digit of the number = x
• Tens digit = (8 - x)

So, given number

⇒ 10 (8 - x) + x

⇒ 80 - 10x + x

⇒ 80 - 9x

If digits are reversed, the number obtained

⇒ 10x + (8 - x)

⇒ 10x + 8 - x

⇒ 9x + 8

According to question :-

⇒ (80 - 9x) + 18 = 9x + 8

⇒ 80 - 9x + 18 = 9x + 8

⇒ 80 + 18 - 9x = 9x + 8

⇒ 98 - 9x = 9x + 8

⇒ 98 - 8 = 9x + 9x

⇒ 90 = 18x

⇒ x = 90/18

⇒ x = 5

Now, given number

⇒ 80 - 9x

⇒ 80 - 9(5)

⇒ 80 - 45

⇒ 35

Hence, the number is 35 .