A man purchase a book and a pen for 25000. He sell the book at 13% P and pen at 17% profit. If he sold the book at 17% profit and pen at 13% profit he earns{ 80. Find their individual cost price.

Options

A. Rs 13500, Rs 11500
B. Rs 12500 Rs 13500
C. Rs23500 Rs 18500
D. Rs 17500 Rs 12500

Answer

To solve the problem step by step, we will denote the cost price of the book as \( B \) and the cost price of the pen as \( P \). We know from the problem statement that:

1. The total cost of the book and pen is \( B + P = 25000 \).
2. The profit from selling the book at 13% and the pen at 17% can be expressed as:
- Selling price of the book = \( B + 0.13B = 1.13B \)
- Selling price of the pen = \( P + 0.17P = 1.17P \)
- Total selling price = \( 1.13B + 1.17P \)

3. The profit earned when selling the book at 17% and the pen at 13% is given as 80:
- Selling price of the book at 17% = \( B + 0.17B = 1.17B \)
- Selling price of the pen at 13% = \( P + 0.13P = 1.13P \)
- Total selling price = \( 1.17B + 1.13P \)

4. The difference in profit between the two selling scenarios is given as:
\[ (1.17B + 1.13P) - (1.13B + 1.17P) = 80 \]

Now, let's simplify the equation:

### Step 1: Set up the equation
\[ (1.17B + 1.13P) - (1.13B + 1.17P) = 80 \]
This simplifies to:
\[ (1.17B - 1.13B) + (1.13P - 1.17P) = 80 \]
\[ 0.04B - 0.04P = 80 \]

### Step 2: Factor out the common term
\[ 0.04(B - P) = 80 \]

### Step 3: Solve for \( B - P \)
Dividing both sides by 0.04:
\[ B - P = \frac{80}{0.04} = 2000 \]

### Step 4: Set up a system of equations
Now we have two equations:
1. \( B + P = 25000 \) (Equation 1)
2. \( B - P = 2000 \) (Equation 2)

### Step 5: Solve the system of equations
Adding Equation 1 and Equation 2:
\[ (B + P) + (B - P) = 25000 + 2000 \]
\[ 2B = 27000 \]
\[ B = 13500 \]

### Step 6: Substitute to find \( P \)
Substituting \( B \) back into Equation 1:
\[ 13500 + P = 25000 \]
\[ P = 25000 - 13500 = 11500 \]

### Final Answer
The cost price of the book is \( 13500 \) and the cost price of the pen is \( 11500 \).