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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.
Solution
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.
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