The ratios of copper to zinc in alloys A and B are 3:4 and 5:9, respectively. If A and B are taken in ratio 2:3 and melted to form new alloy C, then the ratio of copper to zinc in C is:

Given, ratios of copper to zinc in alloys A and B are 3:4 and 5:9,respectively.

So, ratio of copper to the total amount in alloy A = $$\dfrac{3}{3+4}=\dfrac{3}{7}$$

Ratio of copper to the total amount in alloy B = $$\dfrac{5}{5+9}=\dfrac{5}{14}$$

Now, if A and B are taken in ratio 2:3,

Ratio of copper to the total amount in alloy C = $$\dfrac{2\left(\dfrac{3}{7}\right)+3\left(\dfrac{5}{14}\right)}{2+3}=\dfrac{\dfrac{6}{7}+\dfrac{15}{14}}{5}=\dfrac{\dfrac{12}{14}+\dfrac{15}{14}}{5}=\dfrac{\dfrac{27}{14}}{5}=\dfrac{27}{14\times\ 5}=\dfrac{27}{70}$$

So, ratio of copper to zinc in alloy C = $$\dfrac{27}{70-27}=\dfrac{27}{43}$$