Question

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. Then what is the number?

Answer 1

Solution :-

Let :-

Digit in ten's place = x

Digit in one's place = y

Two digit number = 10x + y

According to the first condition :-

$\longrightarrow \sf x+y = 9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According to the second condition :-

$\longrightarrow \sf 10x+y+27 = 10y+x \\\\\longrightarrow 10x-x+y-10y = -27 \\\\\longrightarrow 9x-9y = -27 \\\\\longrightarrow x-y = -3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(2)$

Equation (2) + Equation (1) :-

$\longrightarrow \sf 2x = 6 \\\\\longrightarrow \bf x = 3$

Substitute the value of x in eq (1) :-

$\longrightarrow\sf 3+y = 9 \\\\\longrightarrow \bf y = 6$

Two digit number = 36

Answer 2

Answer:

✯ Given :-

• The sum of the digits of two digits number is 9.
• If 27 is added to it, the digits of the number get reversed.

✯ To Find :-

• What is the number.

✯ Solution :-

» Let, the digits in the tens place be x » And, digits in the ones place be ySum of the digit is 9

➙ Hence, we have,

➣ x + y = 9 ........ ❶

The two digit number is 10x + y

➣ According to the question,

⇒ 10x + y + 27 = 10y + x

⇒ 9x - 9y = - 27

⇒ x - y = - 3 ...... ❷

On substracting equation no 2 from 1 and eliminating y we get,

⇒ 2x + 6

⇒ x = 3

On substituting value of x in the equation no 1 we get,

⇒ x + y = 9

⇒ 3 + y = 9

⇒ y = 9 - 3

⇒ y = 6

So, the number is 10x + y = 10 × 3 + 6 = 36

$\therefore$ The two digits number is 36 .