Ashwin distributed 75 sweets amongst Shweta, Pallavi, and Geeta in the ratio `3:4:8`. Find how many and what percentage of sweets did each get.

Answer

To solve the problem of how Ashwin distributed 75 sweets among Shweta, Pallavi, and Geeta in the ratio of 3:4:8, we can follow these steps:

### Step 1: Understand the Ratio
The ratio of sweets distributed is given as 3:4:8. This means:
- Shweta gets 3 parts,
- Pallavi gets 4 parts,
- Geeta gets 8 parts.

### Step 2: Calculate the Total Parts
To find the total number of parts in the ratio, we add the parts together:
\[ 3 + 4 + 8 = 15 \]
So, there are a total of 15 parts.

### Step 3: Determine the Value of One Part
Since the total number of sweets is 75, we can find the value of one part by dividing the total sweets by the total parts:
\[ \text{Value of one part} = \frac{75}{15} = 5 \]

### Step 4: Calculate the Number of Sweets for Each Person
Now, we can calculate the number of sweets each person gets by multiplying the number of parts they receive by the value of one part.

- **Shweta's sweets**:
\[ \text{Shweta} = 3 \times 5 = 15 \]

- **Pallavi's sweets**:
\[ \text{Pallavi} = 4 \times 5 = 20 \]

- **Geeta's sweets**:
\[ \text{Geeta} = 8 \times 5 = 40 \]

### Step 5: Calculate the Percentage of Sweets Each Person Received
To find the percentage of sweets each person received, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Number of sweets}}{\text{Total sweets}} \right) \times 100 \]

- **Shweta's percentage**:
\[ \text{Percentage of Shweta} = \left( \frac{15}{75} \right) \times 100 = 20\% \]

- **Pallavi's percentage**:
\[ \text{Percentage of Pallavi} = \left( \frac{20}{75} \right) \times 100 = \frac{2000}{75} = \frac{80}{3} \approx 26.67\% \]

- **Geeta's percentage**:
\[ \text{Percentage of Geeta} = \left( \frac{40}{75} \right) \times 100 = \frac{4000}{75} = \frac{160}{3} \approx 53.33\% \]

### Final Summary
- Shweta received **15 sweets**, which is **20%** of the total.
- Pallavi received **20 sweets**, which is approximately **26.67%** of the total.
- Geeta received **40 sweets**, which is approximately **53.33%** of the total.