A woman buys toffees at Rs 2.50 a dozen and an equal number at Rs 3 a score. She sells them at Rs 3.60 a score and thus makes a profit of Rs 10. How many toffees did she buy?

Options

A. 10000
B. 12000
C. 5000
D. 6000

Answer

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

### Step 1: Understand the Cost of Toffees
The woman buys toffees at two different rates:
1. At Rs 2.50 a dozen (12 toffees).
2. At Rs 3.00 a score (20 toffees).

Let the number of dozens of toffees she buys at Rs 2.50 be \( x \). Therefore, the number of toffees bought at this rate is \( 12x \).

The number of scores of toffees she buys at Rs 3.00 is also \( x \). Therefore, the number of toffees bought at this rate is \( 20x \).

### Step 2: Total Number of Toffees
Since she buys an equal number of toffees at both rates:
- Total number of toffees = \( 12x + 20x = 32x \).

### Step 3: Calculate the Total Cost Price
1. Cost of toffees bought at Rs 2.50 per dozen:
\[ \text{Cost} = x \times 2.50 = 2.50x \]
2. Cost of toffees bought at Rs 3.00 per score:
\[ \text{Cost} = x \times 3 = 3x \]
3. Total Cost Price (CP):
\[ \text{Total CP} = 2.50x + 3x = 5.50x \]

### Step 4: Selling Price Calculation
The woman sells the toffees at Rs 3.60 per score (20 toffees):
- Selling price for \( x \) scores:
\[ \text{Selling Price (SP)} = x \times 3.60 = 3.60x \]
- Total Selling Price for all toffees:
\[ \text{Total SP} = 3.60x \]

### Step 5: Profit Calculation
According to the problem, the profit made is Rs 10. The profit can be expressed as:
\[ \text{Profit} = \text{Total SP} - \text{Total CP} \]
Substituting the values we have:
\[ 10 = 3.60x - 5.50x \]
\[ 10 = -1.90x \]

### Step 6: Solve for \( x \)
Rearranging the equation gives:
\[ 1.90x = 10 \]
\[ x = \frac{10}{1.90} \approx 5.26 \]

### Step 7: Total Number of Toffees
Now, substituting \( x \) back to find the total number of toffees:
\[ \text{Total Toffees} = 32x = 32 \times 5.26 \approx 168.32 \]

Since the number of toffees must be a whole number, we round it to the nearest whole number, which is 168 toffees.

### Final Answer
The total number of toffees she bought is approximately **168 toffees**.

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