Two alloys of gold and copper are mixed in the ratio 2:3. The first alloy has gold and copper in the ratio 4:1, and the second in the ratio 1:4. What is the ratio of gold to copper in the resulting mixture?

Correct option is A

Given:
Ratio in which the two alloys are mixed = 2 : 3
Ratio of gold to copper in the first alloy = 4 : 1
Ratio of gold to copper in the second alloy = 1 : 4
Formula Used:
Quantity of component = $$\frac{Ratio\ part}{Total\ ratio\ parts}$$​ × Total quantity
Solution:
Let the quantities of the two alloys taken be 20 units and 30 units respectively to match the 2:3 ratio and make calculations easier.
In the first alloy (20 units), the ratio of gold to copper is 4 : 1. The total parts are 5.
Gold in first alloy = $$\frac{4}{5}$$​ × 20 = 16
Copper in first alloy = $$\frac{1}{5}$$​ × 20 = 4
In the second alloy (30 units), the ratio of gold to copper is 1 : 4. The total parts are 5.
Gold in second alloy = $$\frac{1}{5}$$​ × 30 = 6
Copper in second alloy = $$\frac{4}{5}$$​ × 30 = 24
Calculate the total gold in the final mixture:
16 + 6 = 22
Calculate the total copper in the final mixture:
4 + 24 = 28
The ratio of gold to copper in the final mixture is 22 : 28 = 11 : 14
Final Answer
So the correct answer is (a)