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)