Discussion
When 75% of a two-digit number is added to it, the digits of the number are reversed. Find the ratio of the unit's digit to the ten's digit in the original number.
Answer: C
Let the number be \( 10t + u \), with \( t \) the tens digit and \( u \) the units digit. Adding 75 per cent of it multiplies it by 1.75, and the result is the reversed number:
\[ 1.75\left(10t + u\right) = 10u + t \]
\[ 17.5t + 1.75u = 10u + t \]
\[ 16.5t = 8.25u \quad\Longrightarrow\quad \frac{u}{t} = \frac{16.5}{8.25} = 2 \]
So the units digit is twice the tens digit, a ratio of 2 : 1. The smallest number fitting is 12, and indeed \( 12 + 0.75(12) = 21 \).
Read the order carefully: the question asks unit to ten, so 1 : 2 is the same relationship stated backwards.
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