Calculating Selling Price with Percentage Gain

This question asks us to find the selling price of an item when the cost price and the percentage gain are given. To solve this, we first need to calculate the amount of gain in rupees and then add it to the cost price to find the selling price.

Understanding Cost Price and Selling Price

The Cost Price (CP) is the price at which an item is purchased. In this case, Qamar purchased the stereo for Rs. 1,500. So, the Cost Price is Rs. 1,500.

The Selling Price (SP) is the price at which an item is sold. This is what we need to find.

Calculating the Gain Amount

Qamar gained 16% on the resale. This gain is calculated on the cost price. To find the actual gain amount in rupees, we calculate 16% of the Cost Price.

Given:

• Cost Price (CP) = Rs. 1,500
• Percentage Gain = 16%

The formula to calculate the gain amount is:

Gain Amount = Percentage Gain of CP

In mathematical terms:

$\text{Gain} = \left(\frac{\text{Percentage Gain}}{100}\right) \times \text{CP}$

Let's substitute the given values:

$\text{Gain} = \left(\frac{16}{100}\right) \times 1500$

$\text{Gain} = \frac{16 \times 1500}{100}$

We can cancel out the two zeros from the numerator and the denominator:

$\text{Gain} = 16 \times 15$

Now, let's calculate $16 \times 15$:

$16 \times 15 = 16 \times (10 + 5) = (16 \times 10) + (16 \times 5)$

$16 \times 10 = 160$

$16 \times 5 = 80$

$160 + 80 = 240$

So, the Gain Amount is Rs. 240.

Finding the Selling Price

The Selling Price is the sum of the Cost Price and the Gain Amount.

Formula:

Selling Price (SP) = Cost Price (CP) + Gain Amount

Substitute the values we know:

$\text{SP} = 1500 + 240$

$\text{SP} = 1740$

Therefore, Qamar sold the stereo for Rs. 1,740.

Summary of Steps

• Identify the Cost Price (CP).
• Identify the Percentage Gain.
• Calculate the Gain Amount (Percentage Gain of CP).
• Calculate the Selling Price (SP = CP + Gain Amount).

Final Answer on Selling Price Calculation

Based on our calculation, the selling price of the used stereo is Rs. 1,740.

Revision Table: Profit and Loss Concepts

Additional Information: Alternative Selling Price Formula

There is also an alternative way to calculate the selling price directly when the cost price and percentage gain are known.

If there is a gain of P%, the selling price can be calculated using the formula:

$\text{SP} = \text{CP} \times \left(\frac{100 + \text{Percentage Gain}}{100}\right)$

Let's apply this formula to the problem:

• CP = Rs. 1,500
• Percentage Gain = 16%

$\text{SP} = 1500 \times \left(\frac{100 + 16}{100}\right)$

$\text{SP} = 1500 \times \left(\frac{116}{100}\right)$

$\text{SP} = \frac{1500 \times 116}{100}$

Cancel out the two zeros from 1500 and 100:

$\text{SP} = 15 \times 116$

Now, let's calculate $15 \times 116$:

$15 \times 116 = 15 \times (100 + 10 + 6) = (15 \times 100) + (15 \times 10) + (15 \times 6)$

$15 \times 100 = 1500$

$15 \times 10 = 150$

$15 \times 6 = 90$

$1500 + 150 + 90 = 1650 + 90 = 1740$

Using this alternative formula also gives the selling price as Rs. 1,740. This confirms our previous calculation.