Ashish supplies bread and jams to a hospital and a school. Bread and jam are supplied in equal number of pieces. Bread comes in a bunch of 8 pieces and Jam comes in a pack of 6 pieces. On a particular day, Ashish has supplied x packets of bread and y packets of jam to the school. On the same day, Ashish has supplied 3x packets of bread along with sufficient packets of jam to hospital. It is known that the number of students in the school are between 500 and 550.
How many packets of bread are supplied in the school?

Options

A. 63 packets
B. 86 packets
C. 65 packets
D. 84 packets

Explanation

To solve the problem, we need to determine how many packets of bread are supplied to the school based on the given conditions.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Bread is supplied in bunches of 8 pieces.
- Jam is supplied in packs of 6 pieces.
- The number of students in the school is between 500 and 550.

2. **Finding the Least Common Multiple (LCM)**:
- To ensure that both bread and jam can be supplied in equal numbers, we need to find the LCM of 6 and 8.
- The prime factorization of 6 is \(2 \times 3\) and for 8 it is \(2^3\).
- The LCM is calculated by taking the highest power of each prime factor:
- \(2^3\) from 8,
- \(3^1\) from 6.
- Thus, LCM = \(2^3 \times 3^1 = 8 \times 3 = 24\).

3. **Finding Multiples of LCM between 500 and 550**:
- We need to find multiples of 24 that lie between 500 and 550.
- The multiples of 24 in this range are:
- \(24 \times 21 = 504\)
- \(24 \times 22 = 528\)
- Therefore, the possible number of students in the school can be either 504 or 528.

4. **Calculating Packets of Bread**:
- Since each packet of bread contains 8 pieces, we can find the number of packets of bread for each case:
- For 504 students:
\[ \text{Packets of bread} = \frac{504}{8} = 63 \]
- For 528 students:
\[ \text{Packets of bread} = \frac{528}{8} = 66 \]

5. **Conclusion**:
- The number of packets of bread supplied to the school can either be 63 or 66.
- Since the question asks for the number of packets of bread supplied to the school, we can conclude that the answer is **63 packets** (as it matches the options provided).

### Final Answer:
The number of packets of bread supplied to the school is **63**.