a vendor bought toffees at 6 for a rupee. how many toffees for a rupee must he sell to gain 30%? 

To solve this, let's break it down step by step:

1. The vendor bought toffees at 6 for a rupee. This means the cost price (C.P.) per toffee is:
   \[
   C.P. = \frac{1}{6} \text{ rupees per toffee.}
   \]

2. The vendor wants to gain 30%. To find the selling price (S.P.) that includes the 30% profit:
   \[
   S.P. = C.P. + 30\% \times C.P.
   \]
   \[
   S.P. = C.P. \times \left(1 + \frac{30}{100}\right) = C.P. \times 1.30
   \]
   \[
   S.P. = \frac{1}{6} \times 1.30 = \frac{1.30}{6} = \frac{13}{60} \text{ rupees per toffee.}
   \]

3. To find how many toffees the vendor must sell for 1 rupee to achieve this profit, we take the reciprocal of the selling price per toffee:
   \[
   \text{Number of toffees per rupee} = \frac{1}{S.P.} = \frac{1}{\frac{13}{60}} = \frac{60}{13} \approx 4.615.
   \]

Thus, the vendor must sell approximately 4.615 toffees for 1 rupee to gain a 30% profit.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the number of toffees change if the profit margin was 20% instead of 30%?
2. What if the vendor had bought toffees at 10 for a rupee, how would that change the selling price for a 30% profit?
3. How much profit in rupees would the vendor make if they sold 100 toffees at the 30% profit rate?
4. If the cost price per toffee increases, how does that affect the number of toffees that must be sold for 1 rupee to maintain the 30% profit?
5. What is the formula for determining the selling price if the desired profit percentage and the cost price are known?

**Tip**: Always check the reciprocal when solving problems related to rates like "how many items per rupee."

A vendor bought toffees at 6 for a rupee. How many toffees for a rupee must he sell to gain 30%?

Learn how to calculate the number of toffees a vendor should sell for 1 rupee to gain a 30% profit. This detailed solution includes key concepts like profit and loss, ratio and proportion, and relevant formulas. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation