Question

An alloy consists of 40$\frac{1}{2}$ g of gold and 5$\frac{1}{4}$ g of silver. Find the ratio by weight of gold to the alloy.

Answer 1

Step 1: Given data in the question

Weight of gold = 40$\frac{1}{2}$ g = $\frac{81}{2}$ g.

Weight of silver = 5 $\frac{1}{4}$g = $\frac{21}{4}$ g.

Weight of alloy = weight of gold + weight of silver

$$\begin{gathered} =\frac{81}{2}+\frac{21}{4} \\ =\frac{(162+21)}{4} \\ =\frac{183}{4}kg \end{gathered}$$

Step 2: Find the ratio by weight of gold to the alloy.

Required Ratio = $\frac{\mathrm{weight}\mathrm{of}\mathrm{gold}}{\mathrm{weight}\mathrm{of}\mathrm{alloy}}$

$$\begin{gathered} =\frac{{\displaystyle \frac{81}{2}}}{{\displaystyle \frac{183}{4}}} \\ =\frac{81x4}{183x2} \\ =\frac{27x2}{61} \\ =\frac{54}{61} \end{gathered}$$

Hence, Required ratio by weight of gold to the alloy. 54:61.