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

Given :

• The sum of the digits of a two digits number is 9.

• 27 is added to it, the digits of the number get reversed.

To find :

• The new number =?

Step-by-step explanation:

Let the ones and ten's digit number of two digits of the number be x and y.

Therefore, two-digit number is = 10x + y

And, the reversed number = 10y + x

According to the question :

➟ x + y = 9

➟ y = 9 – x ..... (1)

Now,

➟ 10y + x - 10x – y = 27 [Given]

➟ 9y – 9x = 27

➟ 9(y - x) = 27

➟ y - x = 27/9

➟ y – x = 3 ..... (2)

Substitute the value of y from eq (1) in eq. (2)

➟ 9 – x – x = 3

➟ 9 – 2x = 3

➟ - 2x = 3 - 9

➟ - 2x = - 6

➟ 2x = 6

➟ x = 6/2

➟ x = 3

Hence, x = 3

So, y = 9 – x = 9 – 3 = 6

Therefore, the two-digit number is = 36.

Answer 2

Answer :

Let the the digit in the tenth place be a and the digit in the one's place is b.

Then,

Original number = 10×a + b

= 10a + b

Reversed number = 10×b + a

= 10b + a

Given, sum of the digits (a+b) = 9

Then, (a + b) = 9__________Equation 1

According to the question,

When 27 is subtracted from the original number then the digits gets reversed ;

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

10a - a + b - 10 b = 27

9a - 9b =27

9(a - b) = 27

(a - b) = 27/9 = 3________Equation 2

Now, from Equation 1 & 2 we can conclude

a + b = 9

a = 9 - b__________Equation 3

By using equation 3 here, we get

a - b = 3

9 - b - b = 3

-2b = 3-9

-2b = - 6

b = 3

And,

a - b = 3

a - 3 = 3

a = 3 +3 = 6

Therefore, the original number is 63.