A man sold a book at 9% profit and a pen at 13% P. If the sold the book at 13% profit and the pen at 9% profit, he gain 80 more. Find the cost price of book and pen if he purchase both at 20,000.

Options

A. Rs 11000,Rs 90000
B. Rs 10000, Rs 8000
C. Rs 9000, Rs 6000
D. Rs 12000,Rs 11000

Answer

To solve the problem step by step, let's define the variables and follow the logic laid out in the video transcript.

### Step 1: Define Variables
Let:
- \( B \) = Cost price of the book
- \( P \) = Cost price of the pen

### Step 2: Set Up the Equations
From the problem, we know:
1. The total cost price of the book and pen is \( B + P = 20,000 \) (Equation 1).
2. When sold at 9% profit for the book and 13% profit for the pen, the profit can be expressed as:
\[ \text{Profit} = 0.09B + 0.13P \]
3. When sold at 13% profit for the book and 9% profit for the pen, the profit can be expressed as:
\[ \text{Profit} = 0.13B + 0.09P \]
4. The difference in profit between these two scenarios is given as \( 80 \):
\[ (0.13B + 0.09P) - (0.09B + 0.13P) = 80 \]

### Step 3: Simplify the Profit Equation
Simplifying the profit equation:
\[ 0.13B + 0.09P - 0.09B - 0.13P = 80 \]
\[ (0.13B - 0.09B) + (0.09P - 0.13P) = 80 \]
\[ 0.04B - 0.04P = 80 \]
Dividing through by 0.04 gives:
\[ B - P = 2000 \quad \text{(Equation 2)} \]

### Step 4: Solve the System of Equations
Now we have two equations:
1. \( B + P = 20,000 \) (Equation 1)
2. \( B - P = 2000 \) (Equation 2)

We can solve these equations simultaneously.

### Step 5: Add the Two Equations
Adding Equation 1 and Equation 2:
\[ (B + P) + (B - P) = 20,000 + 2000 \]
\[ 2B = 22,000 \]
\[ B = 11,000 \]

### Step 6: Substitute to Find \( P \)
Now substitute \( B \) back into Equation 1 to find \( P \):
\[ 11,000 + P = 20,000 \]
\[ P = 20,000 - 11,000 = 9,000 \]

### Final Answer
The cost price of the book is \( 11,000 \) and the cost price of the pen is \( 9,000 \).