Question

Consider the ratios related as $ 3:x=x:75 $ then what is the value of x.
(a) 15
(b) 25
(c) 9
(d) 35

Answer 1

Hint: The expression $ x:y $ can also be expressed as the fraction $ \dfrac{x}{y} $ we need to rearrange the equation in such a way from where we can easily find the value of x. Rearrange the given equation to find the value of $ {{x}^{2}} $ first, then from $ {{x}^{2}} $ we can easily find out the value x.

Complete step-by-step answer:
It is given that,
 $ 3:x=x:75 $
The expression $ x:y $ can also be expressed as the fraction $ \dfrac{x}{y} $ , hence given equation can also be written as,
 $ \dfrac{3}{x}=\dfrac{x}{75} $
Now, we need to rearrange the equation by cross multiplication,
 $ \dfrac{3}{x}=\dfrac{x}{75} $
 $ x\times x=75\times 3 $
 $ {{x}^{2}}=225 $
To find the value of $ x $ from above equation we will have to take square root on both sides,
 $ {{x}^{2}}=225 $
 $ \sqrt{{{x}^{2}}}=\sqrt{225} $
we’ll get two values of x one with positive sign and other with negative,
 $ x=\pm 15 $
Value of $ x $ comes out to be 15 or -15.
So, the correct answer is “Option A”.

Note: One needs to be careful in calculations while solving these types of questions. It is very easy to mess up while solving, even one simple calculation error can lead to wrong answers and will make your time short for the rest of the questions in the exam.You should always be attentive while taking square roots on both sides. We will get two values of any variable we are solving for one positive and other negative. Most students miss out one or the other value. This was an objective type question so there was nothing much but this can lead to serious error in bigger problems while solving them.