Question

Study the pattern and write next step:
\[\begin{align}
  & 24\times 5=120\times 1 \\
 & 24\times 15=120\times 3 \\
 & 24\times 25=120\times 5 \\
 & 24\times 35=120\times 7 \\
\end{align}\]
(a)$24\times 5=120\times 1$
(b)$24\times 45=120\times 9$
(c)$24\times 5=120\times 2$
(d)$24\times 25=120\times 4$

Answer 1

Hint: For solving this problem, we first try to make an observable pattern between both the series. By obtaining such a pattern, we can easily identify the next term occurring in the pattern. Using this methodology, we can proceed for getting our answer.

Complete step-by-step answer:
According to our problem, we are given an observable pattern such that:
\[\begin{align}
  & 24\times 5=120\times 1 \\
 & 24\times 15=120\times 3 \\
 & 24\times 25=120\times 5 \\
 & 24\times 35=120\times 7 \\
\end{align}\]
Now, we can express left-hand side in simplified form as:
$\begin{align}
  & 24\times 5\times 1 \\
 & 24\times 5\times 3 \\
 & 24\times 5\times 5 \\
 & 24\times 5\times 7 \\
\end{align}$
Also, the right-hand side can be simplified as:
$\begin{align}
  & 24\times 5\times 1 \\
 & 24\times 5\times 3 \\
 & 24\times 5\times 5 \\
 & 24\times 5\times 7 \\
\end{align}$
Now, our relationship is obtained between L.H.S and R.H.S of the provided data.
Now, increasing the value on left-hand side or right-hand side by one step, we get
\[\begin{align}
  & 24\times 5\times 9=120\times 9 \\
 & 24\times 45=120\times 9 \\
\end{align}\]
Therefore, option (b) is correct.

Note: This problem can be alternatively solved by observing the pattern carefully. We can easily find the increment in right-hand side and left-hand side without simplifying any value and hence obtain our answer.