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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
Question

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?

A.

11:14

B.

13:12

C.

17:28

D.

19:26

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 = Ratio partTotal ratio parts \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 = 45 \frac{4}{5}​ × 20 = 16
Copper in first alloy = 15 \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 = 15 \frac{1}{5}​ × 30 = 6
Copper in second alloy = 45\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)

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