Tanu sells 15 bicycles at a profit of Rs 754 per bicycle and sells 5 bicycles at a loss of Rs 364 per bicycle. If the total profit percentage on all the bicycles sold is 25%, the cost price (in Rs) per bicycle is:

Options

A. 1898
B. 1728
C. 1960
D. 1190

Answer

To find the cost price per bicycle, we can follow these steps:

### Step 1: Define the Variables
Let the cost price of one bicycle be \( x \) rupees.

### Step 2: Calculate the Profit from Selling Bicycles
Tanu sells 15 bicycles at a profit of Rs 754 per bicycle. Therefore, the total profit from these bicycles is:
\[ \text{Total Profit from 15 Bicycles} = 15 \times 754 = 11310 \text{ rupees} \]

### Step 3: Calculate the Loss from Selling Bicycles
Tanu sells 5 bicycles at a loss of Rs 364 per bicycle. Therefore, the total loss from these bicycles is:
\[ \text{Total Loss from 5 Bicycles} = 5 \times 364 = 1820 \text{ rupees} \]

### Step 4: Calculate the Total Profit
The total profit from all 20 bicycles sold (15 sold at profit and 5 sold at loss) is:
\[ \text{Total Profit} = \text{Total Profit from 15 Bicycles} - \text{Total Loss from 5 Bicycles} \]
\[ \text{Total Profit} = 11310 - 1820 = 9490 \text{ rupees} \]

### Step 5: Relate Total Profit to Cost Price
According to the problem, the total profit percentage on all bicycles sold is 25%. Therefore, we can express this as:
\[ \text{Total Profit} = 25\% \text{ of Total Cost Price} \]
The total cost price for 20 bicycles is:
\[ \text{Total Cost Price} = 20x \]
Thus, we can write:
\[ 9490 = \frac{25}{100} \times 20x \]

### Step 6: Simplify the Equation
Rearranging the equation gives:
\[ 9490 = \frac{5}{100} \times 20x \]
\[ 9490 = \frac{100}{100} \times x \]
\[ 9490 = 5x \]

### Step 7: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{9490}{5} = 1898 \text{ rupees} \]

### Conclusion
The cost price per bicycle is Rs 1898.

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