Oranges are bought at 7 for Rs. 3 At what rate per hundred must they be sold to gain 33%?

Options

A. Rs. 56
B. Rs. 60
C. Rs. 58
D. Rs.57

Answer

To solve the problem of determining the selling price per hundred oranges to achieve a 33% gain, we can follow these steps:

### Step 1: Determine the Cost Price of One Orange
The cost price of 7 oranges is given as Rs. 3. Therefore, the cost price of one orange can be calculated as:

\[ \text{Cost Price of 1 Orange} = \frac{3 \text{ Rs}}{7} = \frac{3}{7} \text{ Rs} \]

**Hint:** To find the cost price of one item, divide the total cost by the number of items.

### Step 2: Calculate the Cost Price of 100 Oranges
To find the cost price of 100 oranges, we multiply the cost price of one orange by 100:

\[ \text{Cost Price of 100 Oranges} = 100 \times \frac{3}{7} = \frac{300}{7} \text{ Rs} \]

**Hint:** To find the total cost for multiple items, multiply the cost of one item by the total number of items.

### Step 3: Calculate the Selling Price for a 33% Gain
To achieve a gain of 33%, we need to calculate the selling price using the formula:

\[ \text{Selling Price} = \left(1 + \frac{\text{Gain Percentage}}{100}\right) \times \text{Cost Price} \]

Substituting the values:

\[ \text{Selling Price} = \left(1 + \frac{33}{100}\right) \times \frac{300}{7} \]

This simplifies to:

\[ \text{Selling Price} = \left(\frac{133}{100}\right) \times \frac{300}{7} \]

**Hint:** To find the selling price with a gain, multiply the cost price by (1 + gain percentage in decimal).

### Step 4: Simplify the Selling Price Calculation
Now, we can simplify the calculation:

\[ \text{Selling Price} = \frac{133 \times 300}{700} = \frac{39900}{700} \]

Now, simplifying \(\frac{39900}{700}\):

\[ \text{Selling Price} = \frac{399}{7} \text{ Rs} \]

**Hint:** When simplifying fractions, divide the numerator and the denominator by their greatest common divisor.

### Step 5: Calculate the Selling Price per 100 Oranges
To find the selling price per 100 oranges, we can directly use the value calculated:

\[ \text{Selling Price per 100 Oranges} = \frac{399}{7} \approx 57 \text{ Rs} \]

**Hint:** The selling price per unit can be directly calculated from the total selling price for the desired quantity.

### Conclusion
Thus, the selling price per hundred oranges to gain a 33% profit is Rs. 57.

**Final Answer:** Rs. 57