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For the original number, let the unit digit and ten’s digit be ‘y’ and ‘x’, respectively.
So, the original number = (10x + y)
Now, if the digits are reversed, the new number = (10y + x).
ATQ, (10x + y) – (10y + x) = 54
Or, 9x – 9y = 54
So, x – y = 6……….(i)
And, given that, x + y = 10………(ii)
By adding equation (i) and equation (ii), we get,
2x = 16
So, ‘x’ = 8
And, ‘y’ = 2
So, the original number = 10x + y = 10 × 8 + 2 = 80 + 2 = 82
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