A and B are two alloys formed by the combination of gold and copper in the ratio 5 : 3 and 5 : 11 respectively. Equal quantities of these two alloys are melted and mixed to form a new alloy C. Now, alloy C contains gold and copper in the ratio:

Correct option is B

Given:

Alloy A is formed by the combination of gold and copper in the ratio 5:3.

Alloy B is formed by the combination of gold and copper in the ratio 5:11.

Equal quantities of alloys A and B are melted and mixed to form a new alloy C.

Solution:

Gold in alloy A: $$\frac{5}{8}$$​ of the total quantity (since 5 parts out of 8 are gold).

Copper in alloy A:$$\frac{3}{8}$$​ of the total quantity.

Gold in alloy B:$$\frac{5}{16}$$​of the total quantity (since 5 parts out of 16 are gold).

Copper in alloy B: $$\frac{11}{16}$$​ of the total quantity.

Let the equal quantity of alloys A and B used in the mixture be x.

Gold in A =$$\frac{5}{8} \times x$$​

Copper in A =$$\frac{3}{8} \times x$$​

Gold in B = $$\frac{5}{16} \times x$$​

Copper in B =$$\frac{11}{16} \times x$$​

Total Gold in Alloy C:

Total Gold = $$\frac{5}{8}x + \frac{5}{16}x = \frac{10}{16}x + \frac{5}{16}x = \frac{15}{16}x$$​

Total Copper in Alloy C:

Total Copper = $$\frac{3}{8}x + \frac{11}{16}x = \frac{6}{16}x + \frac{11}{16}x = \frac{17}{16}x$$​​

Ratio of Gold to Copper =$$\frac{\frac{15}{16}x}{\frac{17}{16}x} = \frac{15}{17}$$​

The ratio of gold to copper in alloy C is 15:17.

Alternate Method: