1077 boxes of oranges were loaded in three trucks. While unloading them 7, 12 and 8 boxes were found rotten in the trucks respectively. If the number of remaining boxes in the three trucks are in the ratio 4:6: 5, find the number of boxes loaded originally in each truck

Answer

To solve the problem, we need to find the number of boxes of oranges originally loaded in each of the three trucks, given the total number of boxes, the number of rotten boxes, and the ratio of the remaining boxes.

### Step-by-Step Solution:

1. **Identify the Total and Rotten Boxes**:
- Total boxes loaded = 1077
- Rotten boxes in Truck A = 7
- Rotten boxes in Truck B = 12
- Rotten boxes in Truck C = 8
- Total rotten boxes = 7 + 12 + 8 = 27

2. **Calculate Remaining Boxes**:
- Remaining boxes = Total boxes - Rotten boxes
- Remaining boxes = 1077 - 27 = 1050

3. **Set Up the Ratio of Remaining Boxes**:
- The remaining boxes in the three trucks are in the ratio 4:6:5.
- Let the remaining boxes in Truck A, B, and C be represented as 4k, 6k, and 5k respectively.

4. **Express Total Remaining Boxes in Terms of k**:
- Total remaining boxes = 4k + 6k + 5k = 15k
- We know from step 2 that Total remaining boxes = 1050.
- Therefore, we can set up the equation: 15k = 1050.

5. **Solve for k**:
- k = 1050 / 15
- k = 70

6. **Calculate Remaining Boxes in Each Truck**:
- Remaining boxes in Truck A = 4k = 4 * 70 = 280
- Remaining boxes in Truck B = 6k = 6 * 70 = 420
- Remaining boxes in Truck C = 5k = 5 * 70 = 350

7. **Find the Original Number of Boxes in Each Truck**:
- Original boxes in Truck A = Remaining boxes + Rotten boxes = 280 + 7 = 287
- Original boxes in Truck B = Remaining boxes + Rotten boxes = 420 + 12 = 432
- Original boxes in Truck C = Remaining boxes + Rotten boxes = 350 + 8 = 358

### Final Answer:
- Original boxes in Truck A = 287
- Original boxes in Truck B = 432
- Original boxes in Truck C = 358