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 students are there in school?

Options

A. 508
B. 504
C. 512
D. 548

Explanation

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step 1: Understand the Problem
We need to find the number of students in the school, which is between 500 and 550. We know that Ashish supplies bread and jam in equal numbers, with bread coming in packs of 8 pieces and jam in packs of 6 pieces.

### Step 2: Find the Least Common Multiple (LCM)
To find out how many pieces of bread and jam we need to supply equally, we should calculate the LCM of the number of pieces in each pack.

- The number of pieces in a pack of bread = 8
- The number of pieces in a pack of jam = 6

To find the LCM of 6 and 8:
- Prime factorization of 6 = 2 × 3
- Prime factorization of 8 = 2^3

Now, take the highest power of each prime:
- For 2, the highest power is 2^3 (from 8)
- For 3, the highest power is 3^1 (from 6)

Thus, the LCM = 2^3 × 3^1 = 8 × 3 = 24.

### Step 3: Find Multiples of LCM Between 500 and 550
Now, we need to find the multiples of 24 that lie between 500 and 550.

- The multiples of 24 are: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, 384, 408, 432, 456, 480, 504, 528, 552, ...

From this list, we can see that the multiples of 24 that fall between 500 and 550 are:
- 504 (24 × 21)
- 528 (24 × 22)

### Step 4: Analyze the Options
The problem states that the number of students is between 500 and 550. The possible multiples we found are 504 and 528.

However, since we need to check the options provided in the question (which are not explicitly listed here), we see that:
- If 504 is an option, it is a valid answer.
- If 528 is also an option, it would also be valid.

Since the video transcript indicates that only 504 is mentioned as matching an option, we conclude:

### Final Answer
The number of students in the school is **504**.

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