Answer :
The solution involves assigning variables to the consecutive odd numbers by ratio , creating an equation from the information given, and solving it to get the smallest number. The largest number is obtained by adding 4 to the smallest number. Finally, the ratio of the smallest to largest is 93 : 97 (option d).
Let the three consecutive odd numbers be x, x+2 and x+4. We are told that the sum of these numbers is equal to 285, so we can create an equation : x + (x + 2) + (x + 4) = 285. Simplifying this equation gives 3x + 6 = 285. Solving for x will give us the smallest number. Subtract 6 from both sides and we get 3x = 279. Divide both sides by 3 gives x = 93. Hence the smallest number is 93 and the largest number is 93+4=97. Therefore, the ratio of the smallest to largest number is 93 : 97, which is option d.
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