24 pencil were at the total cost of rs 240 and sold at the rate of 96 per dozen. find the profit and loss percentage 

To find the profit or loss percentage, we’ll go through the following steps:

1. **Calculate the Cost Price (CP)**:
   - Total cost of 24 pencils = Rs 240.
   - So, the cost price of one pencil = \( \frac{240}{24} = 10 \) rupees.

2. **Calculate the Selling Price (SP)**:
   - Selling price is given as Rs 96 per dozen.
   - One dozen equals 12 pencils, so the selling price per pencil = \( \frac{96}{12} = 8 \) rupees.

3. **Calculate Profit or Loss**:
   - Since the selling price per pencil (Rs 8) is less than the cost price per pencil (Rs 10), there is a **loss**.
   - Loss per pencil = \( 10 - 8 = 2 \) rupees.
   - Total loss for 24 pencils = \( 24 \times 2 = 48 \) rupees.

4. **Calculate Loss Percentage**:
   - Loss percentage = \( \frac{\text{Total Loss}}{\text{Total Cost Price}} \times 100 \)
   - Loss percentage = \( \frac{48}{240} \times 100 = 20\% \)

### Answer
The loss percentage is **20%**.

Would you like further clarification on any step?

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Here are 5 related questions for practice:

1. If the selling price were increased to Rs 120 per dozen, what would be the new profit or loss percentage?
2. What would be the profit or loss percentage if the cost price was Rs 200 for 24 pencils and selling price remained the same?
3. If the selling price was Rs 8 per pencil, how much should the cost price per pencil be to achieve a 10% profit?
4. How many pencils need to be sold at Rs 96 per dozen to cover a total cost of Rs 300?
5. If a loss of 15% was expected, what would the selling price per pencil need to be?

#### Tip:
When calculating percentage gain or loss, always divide the profit or loss by the **initial cost price** to avoid errors.

24 pencils were at the total cost of Rs 240 and sold at the rate of Rs 96 per dozen. Find the profit and loss percentage.

Solve a profit and loss percentage problem involving 24 pencils bought for Rs 240 and sold at Rs 96 per dozen. Learn how to calculate cost price, selling price, and loss percentage step-by-step. This is a practical exercise on percentages suitable for Grades 6-8.

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