By selling 15 pencils for Rs.30, Rajan lost 20%. How many pencils should he sell for Rs.52 to have
a gain of 30%?

Let's solve the problem step by step.

### Step 1: Determine the Cost Price (CP) per pencil.
Rajan sold 15 pencils for Rs. 30 at a loss of 20%. To find the Cost Price (CP) of 15 pencils, we first need to calculate the Selling Price (SP) at no loss or gain (100% of the CP):

Since there's a 20% loss, it means he sold them for 80% of the actual CP.

\[
\text{SP of 15 pencils} = \text{CP of 15 pencils} \times \frac{80}{100}
\]

Given that the SP of 15 pencils is Rs. 30, we can write:

\[
30 = \text{CP of 15 pencils} \times \frac{80}{100}
\]

To find the CP of 15 pencils:

\[
\text{CP of 15 pencils} = \frac{30 \times 100}{80} = \frac{3000}{80} = 37.5 \text{ Rs.}
\]

Now, the CP per pencil is:

\[
\text{CP per pencil} = \frac{37.5}{15} = 2.5 \text{ Rs.}
\]

### Step 2: Determine the Selling Price (SP) for a 30% gain.
To find the selling price that would give a 30% gain, we calculate:

\[
\text{SP per pencil} = \text{CP per pencil} \times \left(1 + \frac{30}{100}\right)
\]

\[
\text{SP per pencil} = 2.5 \times 1.3 = 3.25 \text{ Rs.}
\]

### Step 3: Determine the number of pencils to sell for Rs. 52.
If the Selling Price per pencil is Rs. 3.25, and Rajan wants to sell pencils for Rs. 52, then the number of pencils \( n \) he should sell is:

\[
n = \frac{52}{3.25} = 16
\]

### Conclusion:
Rajan should sell **16 pencils** for Rs. 52 to have a gain of 30%.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. What would be the selling price if Rajan wants to gain 50%?
2. How many pencils should be sold for Rs. 100 to achieve a 40% gain?
3. If Rajan had sold the pencils for Rs. 35, what would his loss percentage be?
4. How much should Rajan sell one pencil for if he wants a 25% profit?
5. What would be the loss if Rajan sold 20 pencils for Rs. 40?
6. How many pencils should Rajan sell for Rs. 60 to neither gain nor lose?
7. What is the break-even price per pencil for Rajan?
8. If Rajan bought the pencils at a 10% discount, how would it affect the selling price for a 30% gain?

**Tip:** To calculate profit or loss percentage, always compare the Selling Price to the Cost Price.

Learn how to calculate the number of pencils Rajan should sell for a 30% profit, solving step-by-step. Rajan initially sold 15 pencils for Rs. 30, incurring a 20% loss. Discover how he can sell pencils for Rs. 52 to gain 30%.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation