Two alloys contain platinum and gold in the ratio of 1:2 and 1:3 respectively. A third alloy C is formed by mixing alloys one and alloy two in the ratio of 3:4.Find the percentage of gold in the mixturea)79.2/7%b)71.2/7%c)73.2/7%d)71.3/7%e)None of theseCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Given information:
- Alloy 1 contains platinum and gold in the ratio of 1:2
- Alloy 2 contains platinum and gold in the ratio of 1:3
- Alloy C is formed by mixing alloys 1 and 2 in the ratio of 3:4

To find: The percentage of gold in the mixture

Solution:
Let us assume that alloy 1 contains 1x units of platinum and 2x units of gold.
Then, alloy 2 contains 1y units of platinum and 3y units of gold.

Now, if we mix alloy 1 and alloy 2 in the ratio of 3:4 to form alloy C, we get:
- 3 units of alloy 1, which contains 3(1x) = 3x units of platinum and 3(2x) = 6x units of gold
- 4 units of alloy 2, which contains 4(1y) = 4y units of platinum and 4(3y) = 12y units of gold

Therefore, alloy C contains 3x + 4y units of platinum and 6x + 12y units of gold.

To find the percentage of gold in the mixture, we need to calculate the ratio of gold to the total weight of the mixture.
Total weight of the mixture = platinum + gold
= (3x + 4y) + (6x + 12y)
= 9x + 16y

Ratio of gold to the total weight of the mixture = (6x + 12y) / (9x + 16y)

Now, we know that alloy 1 has a gold to platinum ratio of 2:1, which means that the percentage of gold in alloy 1 is:
gold% in alloy 1 = (2x / (1x + 2x)) x 100
= 66.67%

Similarly, the percentage of gold in alloy 2 is:
gold% in alloy 2 = (3y / (1y + 3y)) x 100
= 75%

Therefore, the weighted average percentage of gold in alloy C is:
weighted average percentage of gold = [(3/7) x 66.67%] + [(4/7) x 75%]
= 70.71%

Hence, the correct answer is option D, 71.3/7%.

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