Question

The sum of the digits of a two - digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find the number.

Answer 1

Let unit’s digit = y

and the ten’s digit = x

So, the original number = 10x + y

The sum of the number = 10x + y

The sum of the digit = x + y

According to the question,

x + y = 15 …(i)

After interchanging the digits, the number = x + 10y

and 10x + y + 9 = x + 10y

⇒ 10x + y + 9 = x + 10y

⇒ 10x – x + y – 10y = – 9

⇒ 9x – 9y = – 9

⇒ x – y = – 1 …(ii)

On adding Eq. (i) and (ii) , we get

x + y + x – y = 15 – 1

⇒ 2x = 14

⇒ x = 7

On substituting the value of x = 5 in Eq. (i), we get

x + y = 15

⇒ 7 + y = 15

⇒ y = 8

So, the Original number = 10x + y

= 10×7 + 8

= 70 + 8

= 78

Hence, the two digit number is 78.