Total cost price of 8 pens and 12 pencils is rs 440.Find at what price 10 pens and 15 pencils should be sell to recieve a profit of 20%.

Let's solve the problem step by step.

### Step 1: Find the total cost of 10 pens and 15 pencils.
The problem states that the total cost price (CP) of 8 pens and 12 pencils is ₹440.

Let's assume:
- The cost price of one pen is \( p \) rupees.
- The cost price of one pencil is \( q \) rupees.

We can set up the following equation based on the given information:
\[
8p + 12q = 440
\]
To find the cost price of 10 pens and 15 pencils, we need to calculate \( 10p + 15q \).

### Step 2: Express \( 10p + 15q \) in terms of \( 8p + 12q \).
Notice that:
\[
10p + 15q = \frac{5}{4} \times (8p + 12q)
\]
This is because:
\[
10p + 15q = \frac{5}{4} \times 8p + \frac{5}{4} \times 12q = \frac{5}{4} \times (8p + 12q)
\]

### Step 3: Substitute the values.
Substitute \( 8p + 12q = 440 \) into the equation:
\[
10p + 15q = \frac{5}{4} \times 440 = 550 \text{ rupees}
\]

### Step 4: Calculate the selling price for a 20% profit.
To achieve a 20% profit, the selling price (SP) should be:
\[
\text{SP} = \text{CP} + 20\% \text{ of CP} = 1.20 \times 550 = 660 \text{ rupees}
\]

### Final Answer:
The selling price of 10 pens and 15 pencils to achieve a 20% profit should be **₹660**.

Would you like more details or have any other questions?

Here are 8 related questions:
1. How would the profit change if the cost price increased by 10%?
2. What would be the selling price if the profit margin were 25%?
3. How would the solution change if the total cost price of 8 pens and 12 pencils was ₹500?
4. How can you determine the individual cost prices of pens and pencils?
5. What if you sold 20 pens and 30 pencils instead?
6. What is the formula for calculating profit percentage?
7. How would a discount on the selling price affect the profit?
8. What is the break-even point for selling these items?

**Tip:** When dealing with percentage increases or decreases in cost or profit, always calculate the new amount by adjusting the original value with the given percentage.

Learn how to calculate the selling price of 10 pens and 15 pencils to achieve a 20% profit. Understand the cost price calculation and apply the profit percentage formula step-by-step.

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