Question

A man has a mass of $120kg$ . He reduces his mass by $15\%$ . How many kilograms is that?

Answer 1

Hint: At first, we write the $15\%$ of $120kg$ as $\dfrac{15}{100}\times 120kg$ . This value gives the reduction value. Finally, subtracting this from the original value, we get the new weight.

Complete step-by-step solution:
It is given that the mass of the man is $120kg$ . Now, the man decides to change his weight. By change, he means reduction. So, the man wants to reduce his weight. Now, he can say the reduction in his weight in various ways. He can say that he has reduced his weight to say $100kg$ . He can also say that he has reduced his weight by $20kg$ . He can also say that he has reduced his weight by ${{\dfrac{1}{6}}^{th}}$ of his weight. Thus, we can see that there are various ways to express the reduction, though all of them mean the same.
We have been told that he has reduced his weight by $15\%$ . Now, by percentage we mean “out of $100$ “. Thus, $15\%$ means $15$ out of $100$ or $\dfrac{15}{100}$ . So, $15\%$ of the mass means,
$\Rightarrow 15\%$ of $120kg$
$\Rightarrow \dfrac{15}{100}\times 120kg$
$\begin{align}
  & \Rightarrow 15\times 1.2kg \\
 & \Rightarrow 18kg \\
\end{align}$
But, the $18kg$ that we have derived is the reduction in his weight. Now,
$\begin{align}
  & \Rightarrow \left( New\text{ }weight \right)\text{ }=\text{ }\left( Old\text{ }weight \right)\text{- }\text{ }\left( Reduction\text{ }in\text{ }weight \right) \\
 & \Rightarrow \left( New\text{ }weight \right)=\left( 120-18 \right)kg \\
 & \Rightarrow \left( New\text{ }weight \right)=102kg \\
\end{align}$
Therefore, we can conclude that the man reduces his weight by $18kg$ and after reduction, his weight becomes $102kg$.

Note: In these percentage increment or decrement problems, we must be careful with the calculations. We should read the question carefully and should note if the reduction percentage is given or the final value as a percentage is given. In this problem, as the reduction percentage is given, we must remember to subtract the $18kg$ at last or our answer will go wrong. Also, there is a shortcut formula for this. The new value will be $\left( 1-\dfrac{15}{100} \right)\times 120kg$ or $102kg$ .