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

1.	he 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 the tens and the units digits of the required number be x and y, respectively. Required number = (10x + y) x + y = 15 ……….(i) Number obtained on reversing its digits = (10y + x) ∴ (10y + x) - (10x + y) = 9 ⇒10y + x – 10x – y = 9 ⇒9y – 9x = 9 ⇒y – x = 1 ……..(ii) On adding (i) and (ii), we get: 2y = 16 ⇒y = 8 On substituting y = 8 in (i) we get x + 8 = 15 ⇒ x = (15 - 8) = 7 Number = (10x + y) = 10 × 7 + 8 = 70 + 8 = 78 Hence, the required number is 78.

he 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 the tens and the units digits of the required number be x and y, respectively.

Required number = (10x + y) x + y = 15 ……….(i)

Number obtained on reversing its digits = (10y + x)

∴ (10y + x) - (10x + y) = 9

⇒10y + x – 10x – y = 9

⇒9y – 9x = 9

⇒y – x = 1 ……..(ii)

On adding (i) and (ii), we get:

2y = 16

⇒y = 8

On substituting y = 8 in (i) we get

x + 8 = 15

⇒ x = (15 - 8) = 7

Number = (10x + y) = 10 × 7 + 8 = 70 + 8 = 78

Hence, the required number is 78.