Question

The ratio of an object’s weight on Earth to its weight on Neptune is $5:7$ . How much would a person who weighs 150 pounds on Earth weigh on Neptune?

Answer 1

Hint: We know that the ratio of the weights of an object on Earth and Neptune is given. So, in order to find the weight of a person on Neptune whose weight on Earth is given, we need to find the Weight of an object on Neptune in terms of the weight of the object when it is calculated on Earth. This can be done using the concept of ratio and proportionality.

Complete answer:
To begin with our solution, let us first assign the known and unknown terms some variables. It will make our calculations easier as we move ahead.
Let the weight of the person when calculated on Earth be ${{W}_{P}}$ .
And, let the weight of the same person when calculated on Neptune be given by : ${{W}_{N}}$ .
Now, it has been given to us in the problem that:
The ratio of an object’s weight on Earth to its weight on Neptune is $=\dfrac{5}{7}$ .
Therefore, we can write that:
$\Rightarrow \dfrac{{{W}_{E}}}{{{W}_{N}}}=\dfrac{5}{7}$
Where, ${{W}_{E}}$ is the weight of the object when calculated on Earth.
On cross multiplying and rearranging terms in the above equation, we get:
$\Rightarrow {{W}_{N}}=\dfrac{7}{5}{{W}_{E}}$
Now, to calculate weight of the person on Neptune, we substitute ${{W}_{E}}={{W}_{P}}$ and put the value of ${{W}_{P}}$ in the above equation.
Therefore, we get:
$\begin{align}
  & \Rightarrow {{W}_{N}}=\left( \dfrac{7}{5}\times 150 \right)lbs \\
 & \Rightarrow {{W}_{N}}=210lbs \\
\end{align}$
Hence, the weight of a person who weighs 150 pounds on Earth is 210 pounds on Neptune.

Note:
It should be noted that these are basic questions of use of ratio and proportion. And one should be able to solve them easily and quickly. We have to be careful when equating the terms in ratio of the two sides. As we could mistakenly write one of them upside them which can make our complete solution incorrect.