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Question
The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. 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 = 12 ……….(i)
Number obtained on reversing its digits = (10y + x)
∴ (10y + x) - (10x + y) = 18
⇒10y + x – 10x – y = 18
⇒9y – 9x = 18
⇒y – x = 2 ……..(ii)
On adding (i) and (ii), we get:
2y = 14
⇒y = 7
On substituting y = 7 in (i) we get
x + 7 = 12
⇒ x = (12 - 7) = 5
Number = (10x + y) = 10 × 5 + 7 = 50 + 7 = 57
Hence, the required number is 57.
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