Question

A 7 metres long rope is $\dfrac{1}{5}$ the length of another rope. How long is the second rope?
A. 5 m
B. 7 m
C. 14 m
D. 35 m

Answer 1

Hint: We will first assume the length of the second rope as x metre. As we are given that the length of the first rope is 7 metres and that the first rope is $\dfrac{1}{5}$ of the length of the second rope, we will form an algebraic equation of this statement as, length of first rope = $\dfrac{1}{5}\times $ length of second rope. We will solve this to get the length of the second rope.

Complete step-by-step answer:
We are given two ropes where the length of 1 rope is given and we have to find the length of the second rope. Also, we have been given a relation between the two ropes, so we will use that relation to find the length of the second rope. Now, it is given that the length of the first rope is 7 metre. So, let us assume the length of the second rope as x metre. Now, we have been given that the length of the first rope is equal to $\dfrac{1}{5}$ of the length of the second rope or, length of first rope = $\dfrac{1}{5}\times $ length of second rope. Now, we will form an algebraic equation with this above statement. So, on substituting the values of length of first rope as 7 metres and length of second rope as x metres, we get,
$\begin{align}
  & 7=\dfrac{1}{5}\times x \\
 & \Rightarrow \dfrac{7}{1}=\dfrac{x}{5} \\
\end{align}$
On cross-multiplying, we will get,
$\begin{align}
  & 1\times x=7\times 5 \\
 & \Rightarrow x=35metres \\
\end{align}$
So, we get the length of the second rope as 35 metres.
Hence, the correct answer is option D.

Note: The possibility of a mistake in this question is that the students can misinterpret the question. They can take the length of the second rope’s length as $\dfrac{1}{5}$ of the length of the first rope and form the algebraic equation as, $x=\dfrac{1}{5}\times 7$ and get the length of the second rope as $\dfrac{7}{5}$ metres, which would be totally incorrect.