Question

A number consists of two digits whose sum is 9.if 27 is subtracted from the number its digits are reversed. Find the numbers?

Answer 1

Let the number be 10 x + y
their sum is 9
therefore  x + y = 9 →  a
 if 27 is subtracted their digits are reversed
⇒ 10 x + y - 27 = 10 y + x
    10 x - x - 27 = 10 y - y
      9 x - 9 y = 27
         x - y = 3 → b

On adding equation a and b
x + y = 9
x - y = 3
2 x = 12
 x = 6

On substituting x = 6 in x + y = 9 we get y = 3
 
The number is 10 x + y = 10(6) + 3 = 63

Answer 2

Answer:

36 or 63 can be the number

Step-by-step explanation:

Assuming

x as tens digit

y as ones digit

Their sum :

x + y = 9 ..... (i)

Number formed :

10x + y

Interchanging the digits :

10y + x

According to the question :

➡ (10x + y) - (10y + x) = 27

➡ 9x - 9y = 27

➡ 9(x - y) = 27

➡ x - y = 27/9

➡ x - y = 3 ..... (ii)

Subtracting both the equation :

$\bf \: x + y = 9 \\ { \underline{ \bf{x - y = 3}}} \\ \implies \bf \: 2x = 6 \\ \implies \bf \: x = 3$

Substituting the value of x in equation (i) :

➡ x + y = 9

➡ 3 + y = 9

➡ y = 6

Hence

The number can be 10x + y

or, 10(3) + 6

or, 36 either 63