If \(\frac{1}{5}: \frac{1}{x}=\frac{1}{x}: \frac{1}{1.25}\), then the value of x will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2.5
In a proportion \(a:b=b:c\), the product of the means equals the product of the extremes. Here the extremes are \(\frac{1}{5}\) and \(\frac{1}{1.25}\), and both means are \(\frac{1}{x}\).
Means multiplied equal extremes multiplied: \(\displaystyle \frac{1}{x}\times\frac{1}{x}=\frac{1}{5}\times\frac{1}{1.25}\)
Since \(5\times1.25=6.25\): \(\displaystyle \frac{1}{x^2}=\frac{1}{6.25}\)
So \(x^2=6.25\) and, taking the positive root, \(x=2.5\)