Let's first find out the amounts of zinc and copper in each of the two types of metals, then we can combine them and find out the overall ratio of zinc to copper in the mixture.

For the first type of metal:

• 2 kg of metal, 1/3 of which is zinc
• So, zinc = (1/3) * 2 kg = 2/3 kg
• Copper = 2 kg - 2/3 kg = (6/3 - 2/3) kg = 4/3 kg

For the second type of metal:

• 3 kg of metal, 1/4 of which is zinc
• So, zinc = (1/4) * 3 kg = 3/4 kg
• Copper = 3 kg - 3/4 kg = (12/4 - 3/4) kg = 9/4 kg

Now, we'll find the total amounts of zinc and copper in the mixture:

• Total zinc = 2/3 kg + 3/4 kg
• Total copper = 4/3 kg + 9/4 kg

To add these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 4 is 12.

• Total zinc = (8/12 + 9/12) kg = 17/12 kg
• Total copper = (16/12 + 27/12) kg = 43/12 kg

Now, we have the total amounts of zinc and copper in the mixture. To find the ratio, we'll divide both by the same number to simplify if possible.

Divide both zinc and copper by the greatest common divisor (GCD) of 17 and 43, which is 1.

• Zinc: 17
• Copper: 43

So, the ratio of zinc to copper in the mixture is 17:43.

Among the given options, the closest one is 17:43.