Multiple choice

In a warehouse, there are eight crates of fruits. The weight of the first crate is 200 kg, and the weight of the second crate is 30% more than the weight of the third crate, which is 15% less than the weight of the first crate. The fourth crate weighs the average of the first and third. The fifth crate weighs the average of the second and fourth. The sixth crate weighs 10% more than the third. The weight of the seventh crate is equal to the average weight of the second and fifth crates, and the weight of the eighth crate is equal to the average weight of all the other crates excluding the second and seventh crate. Find the average of the average weight of the five lighter crates and the average weight of the five heavier crates.

  1. 189.35 kg

  2. 186 kg

  3. 195.60 kg

  4. 276 kg

  5. 391.20 kg
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C Correct answer
Explanation

Crate 1 = 200. Crate 3 = 200 * 0.85 = 170. Crate 2 = 170 * 1.3 = 221. Crate 4 = (200 + 170) / 2 = 185. Crate 5 = (221 + 185) / 2 = 203. Crate 6 = 170 * 1.1 = 187. Crate 7 = (221 + 203) / 2 = 212. Crate 8 = (200 + 170 + 185 + 203 + 187) / 5 = 189. The weights are 200, 221, 170, 185, 203, 187, 212, 189. Sorted: 170, 185, 187, 189, 200, 203, 212, 221. The five lighter are 170, 185, 187, 189, 200 (avg 186.2). The five heavier are 189, 200, 203, 212, 221 (avg 205). The average of these two averages is (186.2 + 205) / 2 = 195.6.

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