Question

sum of dgits of a two digit number is 9. When the digits are reversed,the new number is 27 more than the original.Find the number​

Answer 1

Answer:

let the two digit number be 10x + y

thus the digit at tens place is x and digit at one's place be y

ATQ

$x + y = 9 (i)\\ 10x + y + 27 = 10y + x \\ 9x - 9y = - 27 \\ x - y = - 3(ii)$

solving equations (i) and (ii) we get,

$2x = 6 \\ x = 3 \\ and \: \: y = 9 - 3 \\ = 6$

hence the required number is 36

Answer 2

Answer:

36

Step-by-step explanation:

Let X and Y be the two digits of the number and,

let 10X + Y be the original number.

We have X + Y = 9 — (i)

According to the question,

10X + Y + 27 = 10Y + X

9X + 27 = 9Y

Dividing both side of the equation by 9, we have:

X + 3 = Y

=> X =Y - 3 — (ii)

Putting (i) and (ii) together, we have:

Y - 3 + Y = 9

2Y = 12

Y = 6

Putting the value of Y on equation (ii), we have:

X = 6 - 3 = 3

Now, the required number = 10X + Y

= 10(3) + 6

= 30 + 6

= 36