Ravish lost 20% by selling a radio set for Rs. 3072. What percent will he gain by selling it for Rs. 4080?

Answer

To solve the problem step by step, we will follow the calculations as outlined in the video transcript.

### Step 1: Determine the Cost Price (CP)
Ravish lost 20% when he sold the radio set for Rs. 3072. We can use the formula for calculating the Cost Price (CP) when we know the Selling Price (SP) and the loss percentage:

\[ CP = \frac{100}{100 - \text{Loss Percentage}} \times SP \]

Substituting the values:

\[ CP = \frac{100}{100 - 20} \times 3072 \]

\[ CP = \frac{100}{80} \times 3072 \]

\[ CP = \frac{5}{4} \times 3072 \]

Calculating \( \frac{5}{4} \times 3072 \):

\[ CP = 5 \times 768 = 3840 \]

### Step 2: Calculate the Gain when Selling for Rs. 4080
Now, we need to find out how much gain Ravish makes when he sells the radio set for Rs. 4080. The gain can be calculated using the formula:

\[ \text{Gain} = SP - CP \]

Substituting the values:

\[ \text{Gain} = 4080 - 3840 = 240 \]

### Step 3: Calculate the Gain Percentage
To find the gain percentage, we use the formula:

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

Substituting the values:

\[ \text{Gain Percentage} = \left( \frac{240}{3840} \right) \times 100 \]

Calculating \( \frac{240}{3840} \):

\[ \text{Gain Percentage} = \left( \frac{1}{16} \right) \times 100 = 6.25\% \]

### Final Answer
Ravish will gain **6.25%** by selling the radio set for Rs. 4080.

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