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
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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