Asked by | 25th May, 2010, 01:35: PM
Let X and Y be the digits, then the number is 10X + Y.
8(X + Y) = 10X + Y .....(1)
which simplifies to,
2X -7Y = 0
2X = 7Y
Hence X + Y = 7Y/2 + Y = 9Y/2 ... (2)
Now the number formed by reversing the digits, 10Y + X.
Hence we can write (1), as, adding 9Y and Subtracting 9X from both sides,
8(X + Y) + 9Y - 9X = 10X + Y + 9Y - 9X
-X + 17Y = 10Y + X
-7Y/2 + 17Y = 10Y + X
27Y/2 = 10Y + X
3(9Y/2) = 10Y + X. ,,, using (2)
But 9Y/2 = X + Y = sum of digits,
3(X + Y) = 10Y + X.
Answered by | 25th May, 2010, 06:23: PM
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