Question : In two types of brass, the ratios of copper to zinc are 8 : 3 and 15 : 7, respectively. If the two types of brass are melted and mixed in the ratio 5 : 2, a new type of brass is obtained. The ratio of copper to zinc in this new type of brass is:
Option 1: 3 : 2
Option 2: 2 : 3
Option 3: 3 : 4
Option 4: 5 : 2
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Correct Answer: 5 : 2
Solution :
Given: In two types of brass, the ratios of copper to zinc are 8 : 3 and 15 : 7.
The two types are melted and mixed in a ratio of 5 : 2.
The ratio of copper to zinc in the first brass = 8 : 3
The ratio of copper to zinc in the second brass = 15 : 7
Copper in the first brass = $\frac{8}{11}$ units
Copper in the second brass = $\frac{15}{22}$ units
Zinc in the first brass = $\frac{3}{11}$ units
Zinc in the second brass = $\frac{7}{22}$ units
Copper in the new type of brass:
$(\frac{8}{11}×\frac{5}{7})+(\frac{15}{22}×\frac{2}{7})=\frac{55}{77}=\frac{5}{7}$ units
Zinc in the new type of brass:
$(\frac{3}{11}×\frac{5}{7})+(\frac{7}{22}×\frac{2}{7})=\frac{22}{77}=\frac{2}{7}$ units
So, the ratio of copper to zinc in the new brass = $\frac{5}{7}:\frac{2}{7}=5:2$
Hence, the correct answer is 5 : 2.
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