Question
A two-digit number decreases by 54 when its digits are
reversed. If the sum of its digits is 10, what is the original number?Solution
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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