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.