Question

the sum of digits of two digit number is 9. if 27 is added to the number get reverse.find the number​

Answer 1

Let the number be xyh

x+y=9 ---------(1)

(10x +y) +27=10y+x

10x-x+y -10y = -27

9x-9y= -27

x-y=-3 ----------(2)

adding (1) and (2)

we get

x=3

substitute in (1)

y=6

so the number is 36

Answer 2

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