Question

An alloy is made up of 48% copper, 24% zinc and the rest is tin. Find the respective weight of each metal in 4.2 kg of the alloy.

Answer 1

Hint: In this question given that the weight of the alloy is 4.2 kg, we will consider the weight of the alloy is equal to 100%. First we will find the value of copper and zinc in alloy by converting percentage to weight (kg) then we subtract the total weight of copper and zinc from the alloy and we get the weight of tin.

Complete step-by-step answer:
We are given that the weight of the alloy is 4.2 kg. Now we will find the number of kg’s of alloy in 1%
$\begin{align}
  & \Rightarrow 4.2kg=100\% \\
 & \Rightarrow 100\%=4.2kg \\
 & \Rightarrow 1\%=\dfrac{4.2}{100}kg \\
 & \Rightarrow 1\%=0.042kg \\
\end{align}$
It is also given that there is 48% of copper is present in the alloy. Therefore, we write the weight of 48% copper in alloy as
$\begin{align}
  & =48\times 0.042kg \\
 & =2.016kg \\
\end{align}$
Also it is given that there is 24% of zinc is present in the alloy. Therefore, we can write the weight of 24% Zinc in alloy as
$\begin{align}
  & =24\times 0.042kg \\
 & =1.008kg \\
\end{align}$
Again, we get the percentage of tin in alloy $=\left( 100\%-48\%-24\% \right)=28\%$
Therefore, we can obtain the weight of 28% tin in alloy is
$\begin{align}
  & =28\times 0.042kg \\
 & =1.176kg \\
\end{align}$
Hence the respective weight of each metal in alloy is 2.016kg of copper, 1.008kg of zinc and 1.176kg of tin.

Note:In the above question we take the whole weight of alloy to 100% and we find the value of 1% in weight of alloy.
Alternative method:
Let the percentage of tin in the alloy be ‘x’
Total alloy = 100%
$\begin{align}
  & \Rightarrow 48\%+24\%+x=100\% \\
 & \Rightarrow 72\%+x=100\% \\
 & \Rightarrow x=100\%-72\% \\
 & \Rightarrow x=28\% \\
\end{align}$
As we get all the percentage of all copper, zinc and tin in the alloy. We can easily get all the values of these by substituting their respective percentage value.