Question

A number consists of two digits whose sum is 9. If 27 is subtracted from the number its
digits are reversed. Find the number.​

Answer 1

Answer:

63

Step-by-step explanation:

Let that two digit number be 'ab' which can also be written as 10a + b.

Here, sum of digit = a + b = 9

b = 9 - a ...(1)

If 27 is subtracted from the number its

digits are reversed(new number becomes 'ba' which can be written as 10b + a).

=> (10a + b) - 27 = 10b + a

=> 10a - a + b - 10b = 27

=> 9a - 9b = 27

=> 9(a - b) = 27

=> a - b = 3, substitute the value from (1)

=> a - (9 - a) = 3

=> 2a = 3 + 9 => 2a = 12

=> a = 6 , therefore b = 9 - a = 9 - 6 = 3

Hence, required number is ab = 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