Question

5. The sum of the digits of a two-digit number is 9. If the digits are interchanged, the number obtained
exceeds the original number by 27. Find the number
TE​

Answer 1

Answer:

The number obtained by interchanging the digits exceeds the original number by 27. Thus, the number is 36.

Answer 2

Answer:

Let the number at the ten's place be x and that at the one's place be y.

Number obtained = 10x + y

The sum of the digits in a two-digits number is 9.

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

The number obtained by interchanging the digits exceeds the original number by 27.

10y + x - ( 10x + y ) = 27

⇒ 10y + x - 10x - y = 27

⇒ 9y - 9x = 27

⇒ y - x = 3 .......(II)

Adding (I) and (II)

x + y = 9

+ - x + y = 3

2y = 12

y = 6

x = 3

Thus, the number is 36.