Three boxes of capacity 24 kg. 36 kg and 84 kg are completely filled with three varieties of wheat A. B and C respectively. All the three boxes were emptled and the three types of wheat were thoroughly mixed and the mixture was put back in the three boxes. How many kg of type A wheat would be there in the third box (in kg)?

Options

A. 10
B. 12
C. 14
D. 16

Answer

To solve the problem step by step, let's break down the information provided and calculate how much of type A wheat would be in the third box after mixing.

### Step 1: Identify the capacities of the boxes
- Box 1 (Type A): 24 kg
- Box 2 (Type B): 36 kg
- Box 3 (Type C): 84 kg

### Step 2: Calculate the total capacity of the boxes
Total capacity = Capacity of Box 1 + Capacity of Box 2 + Capacity of Box 3
Total capacity = 24 kg + 36 kg + 84 kg = 144 kg

### Step 3: Determine the ratio of each type of wheat
The ratio of the types of wheat based on the original capacities is:
- Type A (from Box 1): 24 kg
- Type B (from Box 2): 36 kg
- Type C (from Box 3): 84 kg

### Step 4: Calculate the total parts in the ratio
Total parts = 24 + 36 + 84 = 144 parts
Thus, the ratio of A:B:C = 24:36:84.

### Step 5: Simplify the ratio
To simplify the ratio, we can divide each part by 12:
- Type A: 24 / 12 = 2
- Type B: 36 / 12 = 3
- Type C: 84 / 12 = 7

So, the simplified ratio is A:B:C = 2:3:7.

### Step 6: Calculate the total parts in the simplified ratio
Total parts = 2 + 3 + 7 = 12 parts.

### Step 7: Determine the amount of type A wheat in the total mixture
Now, we need to find out how much of type A wheat is in the total mixture of 144 kg:
- Amount of type A wheat = (2/12) * 144 kg = 24 kg.

### Step 8: Determine how much of type A wheat is in the third box
Since the total amount of type A wheat is 24 kg and we are redistributing the wheat based on the original capacities:
- Box 3 has a capacity of 84 kg, which is the largest box. The proportion of type A wheat in the total mixture will remain the same.

To find out how much type A wheat is in Box 3:
- The proportion of type A wheat in the total mixture is 24 kg out of 144 kg.
- The amount of type A wheat in Box 3 = (Capacity of Box 3 / Total Capacity) * Total amount of type A wheat
- Amount of type A in Box 3 = (84 / 144) * 24 kg = 14 kg.

### Final Answer
Thus, the amount of type A wheat in the third box is **14 kg**.

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