By selling 32 oranges for Rs. 30 a man loses 25%. How many oranges should be sold for Rs. 24 so as to gain 20% in the transaction?

Options

A. 16
B. 24
C. 32
D. 28

Answer

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

### Step 1: Determine the Cost Price (CP) of 32 Oranges
Given that selling 32 oranges for Rs. 30 results in a loss of 25%, we can use the formula for loss:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} - \text{Loss} \]

Since a loss of 25% means the selling price is 75% of the cost price, we can express this as:

\[ SP = 0.75 \times CP \]

Substituting the selling price:

\[ 30 = 0.75 \times CP \]

### Step 2: Calculate the Cost Price (CP)
Now, we can solve for CP:

\[ CP = \frac{30}{0.75} = 40 \]

So, the cost price of 32 oranges is Rs. 40.

### Step 3: Determine the Cost Price of One Orange
To find the cost price of one orange, we divide the total cost price by the number of oranges:

\[ \text{Cost Price of 1 Orange} = \frac{CP}{32} = \frac{40}{32} = 1.25 \]

### Step 4: Determine the Selling Price for a 20% Gain
To gain 20%, we need to calculate the selling price (SP) using the formula:

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

Where gain is 20% of the cost price:

\[ \text{Gain} = 0.20 \times CP = 0.20 \times 40 = 8 \]

Thus, the selling price for a gain of 20% is:

\[ SP = 40 + 8 = 48 \]

### Step 5: Determine the Number of Oranges to Sell for Rs. 24
Now, we need to find out how many oranges should be sold for Rs. 24 to achieve this selling price.

If we sell \( x \) oranges for Rs. 24, the selling price per orange is:

\[ \text{Selling Price per Orange} = \frac{24}{x} \]

We want this to equal the selling price per orange that gives us a 20% gain:

\[ \frac{24}{x} = 1.5 \]

### Step 6: Solve for \( x \)
Now, we can solve for \( x \):

\[ 24 = 1.5x \]

\[ x = \frac{24}{1.5} = 16 \]

### Conclusion
Thus, to gain 20%, the man should sell **16 oranges for Rs. 24**.

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