A box of 10 pencils is sold for Rs 22 at 10 percent profit. Calculate cost price of each pencil?

To calculate the cost price of each pencil, let's follow these steps:

1. **Determine the Selling Price (SP) of the box:**
   - The box of 10 pencils is sold for Rs 22.
   - This selling price includes a 10% profit.

2. **Calculate the Cost Price (CP) of the box:**
   - Let the cost price of the box be \( x \) rupees.
   - The selling price \( SP \) is given by:
     \[
     SP = CP + \text{Profit}
     \]
   - Given that the profit is 10% of the cost price:
     \[
     \text{Profit} = \frac{10}{100} \times CP = 0.1 \times x
     \]
   - So, the selling price becomes:
     \[
     SP = x + 0.1x = 1.1x
     \]
   - We know \( SP = Rs 22 \), so:
     \[
     1.1x = 22
     \]

3. **Solve for the Cost Price \( x \) of the box:**
   \[
   x = \frac{22}{1.1} = 20
   \]
   - So, the cost price of the box of 10 pencils is Rs 20.

4. **Calculate the Cost Price per Pencil:**
   \[
   \text{Cost price per pencil} = \frac{20}{10} = Rs 2
   \]

Therefore, the cost price of each pencil is Rs 2.

Would you like any details or have any questions? Here are some related questions:

1. If the selling price per pencil was Rs 2.50, what would the profit percentage be?
2. What would be the selling price if the profit was increased to 15%?
3. How would the cost price change if the profit percentage was reduced to 5%?
4. If the cost price per pencil increased by Rs 0.50, what would the new selling price be to maintain the 10% profit?
5. What is the total profit earned from selling 50 pencils at the same profit percentage?

**Tip:** Always verify if the percentage given is based on cost price or selling price to avoid calculation errors.

Learn how to calculate the cost price of each pencil when a box of 10 pencils is sold for Rs 22 at a 10% profit. Follow a detailed step-by-step solution covering profit and loss concepts and percentage calculations. Suitable for Grades 7-9.

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