To calculate the percentage of peanuts in the new mixture, we need to calculate the total weight of peanuts in the mixture and divide it by the total weight of the new mixture.
First, we need to calculate the weight of peanuts in the 4 kg mixture of nuts:
Weight of peanuts in 4 kg mixture = 4 kg x 0.16 = 0.64 kg
Next, we need to calculate the weight of peanuts in the 12 kg mixture of nuts:
Weight of peanuts in 12 kg mixture = 12 kg x 0.40 = 4.8 kg
The total weight of peanuts in the new mixture will be the sum of the weight of peanuts in the two mixtures:
Total weight of peanuts in new mixture = 0.64 kg + 4.8 kg = 5.44 kg
The total weight of the new mixture will be the sum of the weights of the two original mixtures:
Total weight of new mixture = 4 kg + 12 kg = 16 kg
Finally, we can calculate the percentage of peanuts in the new mixture by dividing the total weight of peanuts by the total weight of the new mixture and multiplying by 100:
Percentage of peanuts in new mixture = (Total weight of peanuts / Total weight of new mixture) x 100 = (5.44 kg / 16 kg) x 100 = 34%
Therefore, the new mixture contains 34% peanuts. Answer choice A is correct.