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 emptied 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, we will follow these instructions:

### Step 1: Identify the capacities of the boxes and the types of wheat.
- The capacities of the boxes are:
- Box 1: 24 kg (filled with wheat A)
- Box 2: 36 kg (filled with wheat B)
- Box 3: 84 kg (filled with wheat C)

### 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 the capacities of the boxes.
- The ratio of the capacities of the boxes is:
- Box 1 : Box 2 : Box 3 = 24 : 36 : 84
- To simplify this ratio, we can divide each term by 12:
- 24 ÷ 12 = 2
- 36 ÷ 12 = 3
- 84 ÷ 12 = 7
- Thus, the simplified ratio is 2 : 3 : 7.

### Step 4: Calculate the total parts in the ratio.
- Total parts = 2 + 3 + 7 = 12 parts.

### Step 5: Determine the amount of type A wheat in the total mixture.
- The amount of type A wheat in the total mixture is based on the ratio:
- Since type A corresponds to 2 parts out of a total of 12 parts, we can calculate the amount of type A wheat:
- Amount of type A wheat = (2/12) * Total capacity
- Amount of type A wheat = (2/12) * 144 kg = 24 kg.

### Step 6: Distribute the type A wheat back into the boxes based on their capacities.
- We need to find out how much type A wheat goes into Box 3 (which has a capacity of 84 kg).
- The ratio of the boxes is 2 : 3 : 7, which means:
- Box 1 (2 parts) will get (2/12) of the total type A wheat,
- Box 2 (3 parts) will get (3/12) of the total type A wheat,
- Box 3 (7 parts) will get (7/12) of the total type A wheat.

### Step 7: Calculate the amount of type A wheat in Box 3.
- Amount of type A wheat in Box 3 = (7/12) * Total amount of type A wheat
- Amount of type A wheat in Box 3 = (7/12) * 24 kg = 14 kg.

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

---