Question

(b) The sum of the digit of a two-digit number is 10. The number formed by reversing the digit is 18
less than the original number. Find the original number.​

Answer 1

Given:

✰ The sum of the digits of a two-digit number is 10.

✰ The number formed by reversing the digit is 18

less than the original number.

To find:

✠ Find the original number.

Solution:

First we will assume that the units digit and tens digit of a number as x and y.

Let the units and tens digit of a number be x and y respectively.

Case 1:

The sum of the digits of a two-digit number is 10 that means we will add both it's digit and it is equal to 10.

➛ x + y = 10

➛ x = 10 - y ...①

Case 2:

The number formed by reversing the digit is 18

less than the original number.

➛ 10x + y + 18 = 10y + x

➛ 10x - x + y - 10y = - 18

➛ 9x - 9y = - 18

➛ 9( x - y ) = - 18

➛ x - y = - 18/9

➛ x - y = - 2

➛ 10 - y - y = - 2 [ Substitute the value of x from eq① ]

➛ -2y = - 2 - 10

➛ -2y = - 12

➛ y = -12/-2

➛ y = 6

Substitute the value of x from eq①

➛ x = 10 - y

➛ x = 10 - 6

➛ x = 4

Now,

➤ The original number = 10y + x

➤ The original number = 10 × 6 + 4

➤ The original number = 60 + 4

➤ The original number = 64

∴ The original number = 64

_______________________________