a person buys some tomatoes at 5 for a rupees and an equal number at 25 np each.he sells them at a rate of 9 for rs 2 but incure a loss of rs 5 in the transaction how may tomatoes did the person purchase? (a) 900 (b) 1500 (c) 1800 (d) 1200

Let's solve this problem step by step.

### Step 1: Understanding the Cost Price
- The person buys some tomatoes at a rate of 5 tomatoes for 1 rupee.
- He buys an equal number of tomatoes at 25 np (paise) each.

#### Conversion of Paise to Rupees:
- 25 np = 0.25 rupees.

### Step 2: Cost Price Calculation
Let's assume he buys \( x \) tomatoes at the rate of 5 for 1 rupee.
- The cost for these \( x \) tomatoes is \( \frac{x}{5} \) rupees.

He also buys an equal number \( x \) of tomatoes at 0.25 rupees each.
- The cost for these \( x \) tomatoes is \( 0.25x \) rupees.

So, the total cost price \( C \) is:
\[
C = \frac{x}{5} + 0.25x = \frac{x}{5} + \frac{x}{4} = \frac{4x + 5x}{20} = \frac{9x}{20} \text{ rupees}
\]

### Step 3: Selling Price Calculation
He sells all these tomatoes at the rate of 9 for 2 rupees.
- The total number of tomatoes is \( 2x \).
- The selling price \( S \) for \( 2x \) tomatoes is:
\[
S = \frac{2x}{9} \times 2 = \frac{4x}{9} \text{ rupees}
\]

### Step 4: Given Loss
The loss is given as 5 rupees, so we have:
\[
\text{Loss} = C - S = 5 \text{ rupees}
\]
Substituting the values of \( C \) and \( S \):
\[
\frac{9x}{20} - \frac{4x}{9} = 5
\]

### Step 5: Solving the Equation
To solve for \( x \), find a common denominator and solve:
\[
\frac{81x}{180} - \frac{80x}{180} = 5
\]
\[
\frac{x}{180} = 5
\]
\[
x = 900
\]

So, the person purchased \( 2x = 2 \times 900 = 1800 \) tomatoes.

### Answer:
The correct answer is **(c) 1800**.

Would you like any further details or have any questions?

Here are 5 related questions for further practice:
1. What would the selling price need to be for the person to make a profit instead?
2. If the number of tomatoes bought at each price differed, how would that affect the outcome?
3. How would the problem change if the loss was Rs 10 instead of Rs 5?
4. What is the total cost price per tomato based on the initial purchase rates?
5. How would the problem change if the selling rate was 10 for Rs 2?

**Tip:** Always double-check unit conversions, especially when working with different currency units like rupees and paise.

Learn how to calculate the number of tomatoes purchased based on cost price and selling price with a loss calculation example. This problem involves understanding cost price per tomato, selling price per lot, and determining the total number of tomatoes bought to incur a specific loss. Suitable for high school students.

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