Question

The Sum of the digits of a 2-digit number is 12.If the digit are reversed the new number obtained is 18
less than the original number. Then, find the original number.​

Answer 1

Answer:

Step-by-step explanation:

Let the tens digit is x and unit digit is y

The number is 10 x + y

(i)

10 x + y - 18 = 10 y + x

9 x - 9 y = 18

x - y = 2

(ii)

x + y = 12

On solving (i) & (ii), we get

x - y = 2

x + y = 12

---------------------

2x = 14

x = 7

Substitute x = 7 in (ii), we get

x + y = 12

7 + y = 12

y = 5

Thus, the original number = 75

Answer 2

Answer:

Let us assume x and y are the two digits of the number

Therefore, two-digit number is = 10x + y and the reversed number = 10y + x

Given:

x + y = 12

y = 12 – x -----------1

Also given:

10y + x - 10x – y = 18

9y – 9x = 18

y – x = 2 -------------2

Substitute the value of y from eqn 1 in eqn 2

12 – x – x = 2

12 – 2x = 2

2x = 10

x = 5

Therefore, y = 12 – x = 12 – 5 = 7

Therefore, the two-digit number is 10x + y = (10*5) + 7 = 57