Question

The sum of the digit of a two digit number is 9 .if 27 is added to the number the digits are reversed. Find the number​

Answer 1

Answer:

36

Step-by-step explanation:

Let the number in the units place be 'x and the number in the tens place be 'y'

Then, x + y = 9     ......(i)

10x + y + 27 = x + 10y

⇒ 10x - x + y - 10y = -27

⇒ 9x - 9y = -27       ......(ii)

Multiplying 9 to equation (i),  9x + 9y = 81  ....(iii)

(ii) + (iii)  ⇒ 9x + 9x - 9y + 9y = 81 - 27

⇒18x = 54

⇒x = 3

Using x = 3 in (i), we get , 3 + y = 9  ⇒ y = 9 - 3 ⇒y = 6

∴ The number is xy = 36

Answer 2

Answer:

Let the number be 10y + x

10y + x + 27 = 10x + y

9y + 27 = 9x

y + 3 = x

The two digit number can be anything as long as the tens digit is 3 more than the units digit.