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. The number is ______.

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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. The number is 78. Explanation: Let the ten’s digit = x and unit’s digit = y. Then x + y = 15 and (10y + x) – (10x + y) = 9 ⇒ 9(y – x) = 9 ⇒ y – x = 1 So, y = x + 1. Substitute: x + (x + 1) = 15 ⇒ 2x = 14 ⇒ x = 7, y = 8 The original number = 10x + y = 78.

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