Question

An alloy of copper and tin consists of 20 parts of tin and 108 parts of copper. Find
the percentage of tin and of copper in the alloy.

Answer 1

Hint: In this problem, we have to find the ratio of the tin and the copper in the alloy. Here, first
we have to find the total parts of metal contained by the alloy. Since the number of parts of tin and
the copper in the alloy is given, we have to add those values to find the total parts. Once we get
the total parts of tin and copper in the alloy, we need to divide the number of parts of tin and the
number of parts of copper with the total amount. This will give the percentage of tin and copper
in the alloy.
Given that the amount of tin in the alloy = 20 parts
The amount of copper in the alloy = 108 parts
Now, we have to add them to get the total parts in the alloy.
Total parts in the alloy
$\begin{array}{c} = 20 + 108\\ = 128\end{array}$

Now, dividing the number of parts of tin and the total number of parts contained by the alloy.
Thus the ratio tin
$\begin{array}{c} = \dfrac{{20}}{{128}}\\ = \dfrac{5}{{32}}\end{array}$

Converting to the percentage, we need to multiply with 100.
Percentage of tin in the alloy
$\begin{array}{c} = \dfrac{5}{{32}} \times 100\\ =
15\dfrac{5}{8}\% \end{array}$

Similarly, dividing the number of parts of copper and the total number of parts contains by the
alloy.
Thus the ratio copper
$\begin{array}{c} = \dfrac{{108}}{{120}}\\ =
\dfrac{{27}}{{32}}\end{array}$

Converting to the percentage.
Percentage of copper in the alloy
$\begin{array}{c} = \dfrac{{27}}{{32}} \times 100\\ =
84\dfrac{3}{8}\% \end{array}$

Hence, the required percentage of tin and copper are $15\dfrac{5}{8}\% $ and
$84\dfrac{3}{8}\% $.

Note: Here, we have to determine the percentage of tin and the copper in the alloy. Since the
number of parts of tin and the number of copper are given, we can calculate the total number of
parts in the alloy. Thus, from that we can find our required percentage.