The sum of two numbers is 74 and their difference is 12. Find the ratio of the smaller number to the larger number.
31 : 43
Let the two numbers be \(x\) (larger) and \(y\) (smaller). Then:
\(x + y = 74\) and \(x - y = 12\)
Adding: \(2x = 86 \Rightarrow x = 43\). Subtracting: \(2y = 62 \Rightarrow y = 31\).
Required ratio = smaller : larger = \(31 : 43\).
The correct answer is : 31 : 43.
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