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# A number consists of two digits whose sum is 9. The number formed by reversing the digits exceeds twice the original number by 18. Find the original Number.

Asked by Abhirami Prabakar 15th December 2013, 7:00 PM
Answered by Expert
Answer:
Let the number be xy = 10x + y
Given: x + y = 9      ... (1)
Reverse number = 2 x Original number + 18
10y + x = 2(10x + y) + 18
10y + x = 20x + 2y + 18
19x - 8y + 18 = 0       ... (2)

Substituting the value of y from (1) in (2), we get,
19x - 8(9 - x) + 18 = 0
19x - 72 + 8x + 18 = 0
27x = 54
x = 2
So, y = 9 - 2 = 7

Thus, the original number is 27.
Answered by Expert 15th December 2013, 10:12 PM
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