Question

A 2cm long grasshopper can jump 160cm. If a 6 meter tall animal had the same height and jump ratio, how far could he jump?
A. 48 m
B. 480 m
C. 180 m
D. 8000 m

Answer 1

Hint: Let us first assume that the 6m tall animal could jump xm. And then transform the unit from centimetre to metre of 2cm and 160cm for the simplification as the unit of the length of the second animal is given in metre. Then, we will apply the ratio formula as it is given that the height and jump ratio are the same.
Formula: $\dfrac{\text{height of grasshopper}}{\text{jump of grasshopper}}=\dfrac{\text{height of }{{\text{2}}^{nd}}\text{ animal}}{\text{jump of }{{\text{2}}^{nd}}\text{ animal}}$

Complete step-by-step answer:
The height of the grasshopper is given = 2cm.
And he can jump up to 160cm.
First, we will transform units of 2cm and 160cm in metre.
As we know that,
\[\begin{align}
  & 1m=100cm \\
 & \Rightarrow 100cm=1m \\
 & \Rightarrow 1cm=\dfrac{1}{100}m \\
\end{align}\]
Applying this formula, we will get,
$\begin{align}
  & 2cm=2\times 1cm \\
 & =2\times \dfrac{1}{100}m \\
 & =0.02m \\
 & And \\
 & 160cm=160\times 1cm \\
 & =160\times \dfrac{1}{100}m \\
 & =1.6m \\
\end{align}$
So, the height of the grasshopper is 0.02m and he could jump upto 1.6m.
Now, the height of the tall animal is 6m and let us assume that he could jump upto xm.
Now, we are given that the height and jump ratio of both animals are same that means,
$\dfrac{\text{height of grasshopper}}{\text{jump of grasshopper}}=\dfrac{\text{height of }{{\text{2}}^{nd}}\text{ animal}}{\text{jump of }{{\text{2}}^{nd}}\text{ animal}}$
Now, by putting the values of each parameter we will get,
$\begin{align}
  & \Rightarrow \dfrac{0.02}{1.60}=\dfrac{6}{x} \\
 & \Rightarrow \dfrac{0.02\times 100}{1.60\times 100}=\dfrac{6}{x} \\
 & \Rightarrow \dfrac{2}{160}=\dfrac{6}{x} \\
 & \Rightarrow \dfrac{1}{80}=\dfrac{6}{x} \\
\end{align}$
By cross multiplication, we will get,
$\begin{align}
  & \Rightarrow 1\times x=80\times 6 \\
 & \Rightarrow x=480m \\
\end{align}$
(As we took x in metres)
So, 6 m tall animal can jump up to 480 m.
Hence, the correct option is (B).

Note: There are chances of mistakes such as students might not think about the unit of length of jump and directly write the answer as 480 cm. We have been given all the details about the grasshopper, so we can get the ratio for grasshoppers. If the students misinterpret the question, they might take the ratio of animals and get the wrong answer.