Question : Three numbers, a, b, and c are said to be in continued proportion if a : b :: b : c. What number must be added to each of the numbers 1, 7 and 25 so that the resulting sums, in that order, maybe in continued proportion?
Option 1: 2
Option 2: 4
Option 3: 6
Option 4: 5
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Correct Answer: 2
Solution : Given: Three numbers, a, b, and c are said to be in continued proportion if a : b :: b : c. When there is a continued proportion, the ratio of the first to the second is the same as the ratio of the second to the third. Let the number to be added be $x$. According to the question, $\frac{1+x}{7+x}=\frac{7+x}{25+x}$ ⇒ $(1+x)(25+x)=(7+x)(7+x)$ ⇒ $25+25x+x+x^2=49+14x+x^2$ ⇒ $12x=24$ ⇒ $x=2$ Hence, the correct answer is 2.
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