Lemons are bought at the rate of 3 for Rs. 4. At what rate must they be sold to gain 20%?

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price (CP)
The lemons are bought at the rate of 3 for Rs. 4. Therefore, the cost price (CP) for 3 lemons is Rs. 4.

### Step 2: Calculate the Profit Percentage
We are given that we need to gain a profit of 20%. This means we need to find the selling price (SP) that includes this profit.

### Step 3: Use the Formula for Selling Price
The formula to calculate the selling price when profit percentage is given is:
\[ SP = CP \times \left(1 + \frac{Profit\%}{100}\right) \]
Substituting the values we have:
\[ SP = 4 \times \left(1 + \frac{20}{100}\right) \]

### Step 4: Simplify the Profit Percentage
Calculating the profit percentage:
\[ \frac{20}{100} = \frac{1}{5} \]
So, we can rewrite the equation as:
\[ SP = 4 \times \left(1 + \frac{1}{5}\right) \]

### Step 5: Convert to a Mixed Number
Now, we need to add 1 and \(\frac{1}{5}\):
\[ 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} \]
Thus, we have:
\[ SP = 4 \times \frac{6}{5} \]

### Step 6: Calculate the Selling Price
Now, multiplying:
\[ SP = \frac{24}{5} \]

### Step 7: Convert to Decimal
To convert \(\frac{24}{5}\) into decimal:
\[ 24 \div 5 = 4.8 \]
Thus, the selling price (SP) is Rs. 4.8.

### Final Answer
The lemons must be sold at Rs. 4.8 to gain a 20% profit.

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