Two alloys $A$ and $B$ contain gold and copper in the ratios of $2:3$ and $3: 7$ by mass, respectively. Equal masses of alloys $A$ and $B$ are melted to make an alloy $C.$ The ratio of gold to copper in alloy $C$ is$:$

1. $5:10$
2. $7:13$
3. $6:11$
4. $9:13$

edited

Alloy A is having Gold and Copper in the ratio 2:3

&

Alloy B is having Gold and Copper in the ratio 3:7

Let's Assume we're taking 1kg of alloy A & 1kg of alloy B

∴ in alloy A Gold will be $\dfrac{2}{5}$ kg

Copper will be $\dfrac{3}{5}$ kg

in alloy B Gold will be $\dfrac{3}{10}$ kg

Copper will be $\dfrac{7}{10}$ kg

In alloy C Gold to Copper ratio will be  ${\dfrac{\dfrac{2}{5} + \dfrac{3}{10}}{\dfrac{3}{5} + \dfrac{7}{10}}}$

= ${\dfrac{\dfrac{7}{10} }{\dfrac{13}{10}}}$

= $\dfrac{7}{13}$

= 7:13    option  (B)

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