Question

Find the value of x in the given series?
 $195:15::x:25$
A. 575
B. 600
C. 625
D. 650

Answer 1

Hint: In this question the series is given $195:15::x:25$.This question is related to the concept of finding the missing term in the given series. Here before solving the question we should observe the pattern involved in the given series. We should observe the relation between the terms of the given series. We should evaluate the value of the next term following the similar relation. For example by observing the given series 195 can be written as${{15}^{2}}-(15\times 2)$.

Complete step-by-step answer:
Before solving this question we can observe the pattern followed by the series given here. From the observed pattern 195 can be written as${{15}^{2}}-(15\times 2)$.We can say that as the 195 is related to the 15 the X is also related to the 25.
 By following the similar relation we can evaluate the value of X.
X can be written as${{25}^{2}}-(25\times 2)$. Let’s simplify this
$\begin{align}
  & 195={{15}^{2}}-(15\times 2) \\
 & \Rightarrow 225-30 \\
 & \Rightarrow 195
\end{align}$
X = ${{25}^{2}}-(25\times 2)$
$\begin{align}
  & \Rightarrow 625-50 \\
 & \Rightarrow 575 \\
 & \Rightarrow x=575 \\
\end{align}$

So, the correct answer is “Option A”.

Note: Here we should carefully observe the series and the pattern involved in it and carefully predicts the next term. If we have a misconception that here $195=15\times 13$ and try to find the value of X following similar to this pattern
$195=15\times 13$
Similarly, let’s find X
$\begin{align}
  & X=25\times 13 \\
 & \Rightarrow 325 \\
 & \Rightarrow X=325
\end{align}$
Hence, the value of X we get in this way is completely wrong.

There is another method to solve this question. We can consider
 $\begin{align}
  & 195=15\times \left( 15-2 \right) \\
 & \Rightarrow 15\times 13
\end{align}$
             $\begin{align}
  & X=25\times \left( 25-2 \right) \\
 & \Rightarrow 25\times 23 \\
 & \Rightarrow 575
\end{align}$
Hence, we will get the correct answer.