A shop man bought pens at the rate of 7 for 10 and sold them at a profit of 40%. How many pens would a customer get for 10 ?Options3465

1. Break Down the Problem

To solve this problem, we need to identify how many pens the customer receives for $10 based on the buying price and the selling price after applying the profit percentage.

2. Relevant Concepts

• The cost price (CP) of pens.
• The selling price (SP) with the profit percentage.
• The formula to calculate profit: $\text{Profit} = \text{SP} - \text{CP}$ or, equivalently, $\text{SP} = \text{CP} \times (1 + \frac{\text{Profit Percentage}}{100})$

3. Analysis and Detail

1. Cost Price Calculation:

   • The shopkeeper buys 7 pens for $10.
   • Therefore, the cost price of one pen is: $\text{CP} = \frac{10}{7} \text{ dollars per pen}$

2. Selling Price Calculation:

   • He sells the pens at a profit of 40%. Therefore, the selling price of one pen is: $\text{SP} = \text{CP} \times (1 + 0.40) = \frac{10}{7} \times 1.40 = \frac{10 \times 1.40}{7} = \frac{14}{7} = 2 \text{ dollars per pen}$

3. Number of Pens for $10:

   • The customer would then receive: $\text{Number of pens} = \frac{10}{\text{SP}} = \frac{10}{2} = 5 \text{ pens}$

4. Verify and Summarize

We verified that the selling price of each pen after calculating the profit is $2, and consequently, for$10, the customer can purchase 5 pens.

Final Answer

A customer would get 5 pens for $10.