For his birthday, Raman brought 65 chocolates, 54 cookies, and 40 pens. How will he distribute them among his 20 classmates so that everyone gets the same number of chocolates, cookies, and pens? Also, calculate the number of chocolates, cookies, and pens still left with Raman.

Answer

To solve the problem of how Raman can distribute 65 chocolates, 54 cookies, and 40 pens among his 20 classmates, we will follow these steps:

### Step 1: Determine how many items each classmate will receive.

To ensure that each of the 20 classmates receives the same number of chocolates, cookies, and pens, we need to divide the total number of each item by the number of classmates.

1. **Chocolates:**
\[ \text{Chocolates per classmate} = \frac{65 \text{ chocolates}}{20 \text{ classmates}} = 3 \text{ chocolates (with a remainder)} \]
Since we cannot give a fraction of a chocolate, we will give 3 chocolates to each classmate.

2. **Cookies:**
\[ \text{Cookies per classmate} = \frac{54 \text{ cookies}}{20 \text{ classmates}} = 2 \text{ cookies (with a remainder)} \]
Similarly, we will give 2 cookies to each classmate.

3. **Pens:**
\[ \text{Pens per classmate} = \frac{40 \text{ pens}}{20 \text{ classmates}} = 2 \text{ pens} \]
Each classmate will receive 2 pens.

### Step 2: Calculate the total distributed items.

Now, we will calculate the total number of items distributed to all classmates.

1. **Total chocolates distributed:**
\[ \text{Total chocolates distributed} = 3 \text{ chocolates/classmate} \times 20 \text{ classmates} = 60 \text{ chocolates} \]

2. **Total cookies distributed:**
\[ \text{Total cookies distributed} = 2 \text{ cookies/classmate} \times 20 \text{ classmates} = 40 \text{ cookies} \]

3. **Total pens distributed:**
\[ \text{Total pens distributed} = 2 \text{ pens/classmate} \times 20 \text{ classmates} = 40 \text{ pens} \]

### Step 3: Calculate the remaining items.

Now we will calculate how many items are left with Raman after distribution.

1. **Remaining chocolates:**
\[ \text{Remaining chocolates} = 65 \text{ chocolates} - 60 \text{ chocolates} = 5 \text{ chocolates} \]

2. **Remaining cookies:**
\[ \text{Remaining cookies} = 54 \text{ cookies} - 40 \text{ cookies} = 14 \text{ cookies} \]

3. **Remaining pens:**
\[ \text{Remaining pens} = 40 \text{ pens} - 40 \text{ pens} = 0 \text{ pens} \]

### Final Summary:

- Each classmate receives:
- 3 chocolates
- 2 cookies
- 2 pens

- Remaining items with Raman:
- 5 chocolates
- 14 cookies
- 0 pens