Understanding the Problem: Calculating Profit on a Used Phone

The question asks us to first figure out the original cost price of a used phone based on its selling price and the percentage loss incurred. Then, we need to calculate the price at which the phone should have been sold to make a specific profit percentage.

We are given:

• Selling Price (SP) = Rs. 6160
• Loss Percentage = 44%
• Target Profit Percentage = 5%

The Selling Price (Rs. 6160) represents the price after a 44% loss on the Cost Price (CP). This means the Selling Price is (100% - 44%) = 56% of the Cost Price.

Step-by-Step Calculation to Find the Original Cost Price

If Rs. 6160 is 56% of the Cost Price, we can set up the following relationship:

\( \text{Selling Price} = \text{Cost Price} \times (100\% - \text{Loss Percentage}) \)

\( 6160 = \text{Cost Price} \times (100\% - 44\%) \)

\( 6160 = \text{Cost Price} \times 56\% \)

\( 6160 = \text{Cost Price} \times \frac{56}{100} \)

To find the Cost Price (CP), we rearrange the equation:

\( \text{Cost Price} = \frac{6160}{\frac{56}{100}} \)

\( \text{Cost Price} = \frac{6160 \times 100}{56} \)

Now, let's perform the division:

\( \text{Cost Price} = \frac{616000}{56} \)

We can simplify this. Dividing 6160 by 56:

\( 6160 \div 56 = 110 \)

So,

\( \text{Cost Price} = 110 \times 100 \)

\( \text{Cost Price} = 11000 \)

The original cost price of the used phone was Rs. 11000.

Calculating the Required Selling Price for a 5% Profit

Now that we know the Cost Price (CP = Rs. 11000), we need to find the Selling Price (New SP) that would result in a 5% profit.

A 5% profit means the Selling Price should be the Cost Price plus 5% of the Cost Price. This is equivalent to 105% of the Cost Price.

\( \text{New Selling Price} = \text{Cost Price} \times (100\% + \text{Profit Percentage}) \)

\( \text{New Selling Price} = 11000 \times (100\% + 5\%) \)

\( \text{New Selling Price} = 11000 \times 105\% \)

\( \text{New Selling Price} = 11000 \times \frac{105}{100} \)

Let's perform the calculation:

\( \text{New Selling Price} = 110 \times 105 \)

Multiplying 110 by 105:

\( 110 \times 105 = 110 \times (100 + 5) = (110 \times 100) + (110 \times 5) \)

\( = 11000 + 550 \)

\( = 11550 \)

So, Rajan should have sold the used phone for Rs. 11550 to make a profit of 5%.

The price at which Rajan should have sold the used phone to make a profit of 5% is Rs. 11550.

Revision Table: Profit and Loss Concepts

Additional Information: Understanding Cost Price and Selling Price

Cost Price (CP): This is the original price at which an item is bought. It includes all initial costs like purchase price, transportation, etc.

Selling Price (SP): This is the price at which an item is sold.

Profit: When the Selling Price is greater than the Cost Price (SP > CP), the difference is a profit. Profit is calculated as SP - CP.

Loss: When the Selling Price is less than the Cost Price (SP < CP), the difference is a loss. Loss is calculated as CP - SP.

Percentages of profit or loss are almost always calculated with respect to the Cost Price, unless specifically mentioned otherwise.

In this problem, the initial sale resulted in a loss because the selling price (Rs. 6160) was less than the original cost price (Rs. 11000). The goal was to find a selling price that would have resulted in a profit of 5% on the original cost price.