By selling 32 oranges for a Rs. a man loss 40%. How many for a rupee did he sell to earn 20%.

Options

A. 0.15
B. 0.22
C. 18
D. 16

Answer

To solve the problem step by step, let's break it down clearly.

### Step 1: Understand the given information
We know that selling 32 oranges for Rs. 4 results in a loss of 40%.

### Step 2: Calculate the Cost Price (CP) of 32 oranges
If there is a loss of 40%, it means the selling price (SP) is 60% of the cost price (CP).

Let the cost price of 32 oranges be \( CP \).

According to the information given:
\[ SP = 60\% \text{ of } CP \]
\[ SP = \frac{60}{100} \times CP \]

Since the selling price is Rs. 4:
\[ 4 = \frac{60}{100} \times CP \]

### Step 3: Solve for Cost Price (CP)
To find \( CP \), we rearrange the equation:
\[ CP = 4 \times \frac{100}{60} = 4 \times \frac{5}{3} = \frac{20}{3} \text{ Rs.} \]

### Step 4: Calculate the Cost Price of 1 orange
To find the cost price of one orange, we divide the total cost price by the number of oranges:
\[ CP \text{ of 1 orange} = \frac{CP}{32} = \frac{20/3}{32} = \frac{20}{96} = \frac{5}{24} \text{ Rs.} \]

### Step 5: Determine the Selling Price (SP) for a 20% profit
To earn a 20% profit, the selling price must be 120% of the cost price.

Let the new selling price of one orange be \( SP' \):
\[ SP' = 120\% \text{ of } CP \text{ of 1 orange} \]
\[ SP' = \frac{120}{100} \times \frac{5}{24} = \frac{6}{5} \times \frac{5}{24} = \frac{6}{24} = \frac{1}{4} \text{ Rs.} \]

### Step 6: Calculate how many oranges can be sold for Rs. 4
To find out how many oranges can be sold for Rs. 4 at the new selling price:
\[ \text{Number of oranges} = \frac{4}{SP'} = \frac{4}{\frac{1}{4}} = 4 \times 4 = 16 \]

### Final Answer
The man sells **16 oranges for Rs. 4** to earn a 20% profit.

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