The sum of the digits of a two - digit number is 15. The number obtain

1.	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» 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.

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»

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.