Alloy A contains copper and zine in the ratio of 4 : 3 and alloy B contains copper and zine in the ratio of 5: 2. A and B are taken in the ratio of 5 : 6 and melted to form a new alloy. The percentage of zinc in the new alloy is closest to:

Ratio of the copper to zinc in alloy A = 4 : 3
Quantity of copper in alloy A = $$\frac{4}{4 + 3} = \frac{4}{7}$$
Quantity of zinc in alloy A = $$\frac{3}{4 + 3} = \frac{3}{7}$$
Ratio of the copper to zinc in alloy B = 5 : 2
Quantity of copper in alloy B = $$\frac{5}{5 + 2} = \frac{5}{7}$$
Quantity of zinc in alloy B = $$\frac{2}{5 + 2} = \frac{2}{7}$$
A and B are taken in the ratio of 5 : 6 and melted to form a new alloy.
So,
Quantity of copper in new alloy = $$5 \times \frac{4}{7} + 6 \times \frac{5}{7} = \frac{20}{7} + \frac{30}{7} = \frac{50}{7}$$
Quantity of zinc in new alloy = $$5 \times \frac{3}{7} + 6 \times \frac{2}{7} =  \frac{15}{7} + \frac{12}{7} = \frac{27}{7}$$
The percentage of zinc in the new alloy = $$\frac{\frac{27}{7}}{\frac{50}{7} + \frac{27}{7}} \times 100 = \frac{27}{77} \times 100 = 35$$%