Question

The number obtained by reversing a two-digit number is 18 more than the original number. If the sum of its digits is 8, find the number.

Answer 1

Answer in the attachment

Answer 2

✬ Number = 53 ✬

Step-by-step explanation:

Given:

• A number obtained by reversing digits is 18 more than original number.
• Sum of digits is 8

To Find:

• What is the number ?

Solution: Let the tens digit of number be x and unit digit be y. Therefore,

➼ Number = 10x + y ,and also it is given that

➼ x + y = 8

➼ x = (8 – y).......(1)

[ Now after reversing the digit the new number formed is ]

➼ Reversed number = 10y + x

A/q

• Reversed number is 18 more than the original number.

$\implies{\rm }$ 10x + y = 10y + x + 18

$\implies{\rm }$ 10x – x = 10y – y + 18

$\implies{\rm }$ 9x = 9y + 18

$\implies{\rm }$ 9(8 – y) = 9y + 18

$\implies{\rm }$ 72 – 9y = 9y + 18

$\implies{\rm }$ 72 – 18 = 9y + 9y

$\implies{\rm }$ 54 = 18y

$\implies{\rm }$ 54/18 = y

$\implies{\rm }$ 3 = y

So,

➬ Unit digit of number = y = 3

➬ Tens digit of number = x = 8 – y

=> 8 – 3 = 5

Hence, the number was 10x + y

➬ 10(5) + 3

➬ 50 + 3 = 53