Three boxes of capacities 24 kg, 36 kg, and 84 kg are completely filled with three varieties of wheat A, B, and C respectively. All three boxes are emptied, the three types of wheat are thoroughly mixed to form a uniform mixture, and then the mixture is put back into the same three boxes, filling them completely again. How many kg of type A wheat will be present in the third box (the 84 kg box)?

Introduction / Context:
This question tests proportional distribution after uniform mixing. When different items are mixed thoroughly, every portion of the new mixture has the same composition as the whole. That means each box receives wheat A in proportion to how large that box is compared to the total amount of mixture. So you find the fraction of wheat A in the total mixture and then apply that same fraction to the capacity of the third box.

Given Data / Assumptions:

• Box 1 capacity = 24 kg (all wheat A)
• Box 2 capacity = 36 kg (all wheat B)
• Box 3 capacity = 84 kg (all wheat C)
• After mixing, composition is uniform everywhere
• Mixture is redistributed back fully into the same capacities

Concept / Approach:
Total wheat quantity = 24 + 36 + 84. Total wheat A in the mixture is still 24 kg (mixing does not change amounts). Fraction of wheat A in the mixture = 24 / total. Wheat A in the 84 kg box = fraction * 84.

Step-by-Step Solution:
Total mixture = 24 + 36 + 84 = 144 kg Total wheat A = 24 kg Fraction of A in mixture = 24 / 144 = 1/6 Wheat A in 84 kg box = (1/6) * 84 = 14 kg

Verification / Alternative check:
Since the third box holds 84 out of 144 kg, it holds 84/144 = 7/12 of the total mixture. Wheat A total is 24, so A in third box should be 24 * (7/12) = 14. Same result, confirming correctness.

Why Other Options Are Wrong:
10 and 12 underestimate the share of A in a large 84 kg box. 16 and 18 overestimate the share and would imply more than 1/6 fraction of A.

Common Pitfalls:
Assuming equal distribution of A into each box, forgetting to compute the total mixture, or using 24/84 instead of 24/144 for the fraction of A.

Final Answer:
The third (84 kg) box will contain 14 kg of wheat type A.