A person bought two bicycles for Rs 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get Rs 5 more. The dilference of the cost price of the two bicycles was:

Options

A. Rs 50
B. Rs40
C. Rs 25
D. Rs 75

Answer

Let's solve the problem step by step.

### Step 1: Define Variables
Let the cost price (CP) of the first bicycle be \( A \) and the cost price of the second bicycle be \( B \).

### Step 2: Set Up the Equation for Total Cost
According to the problem, the total cost of the two bicycles is:
\[ A + B = 1600 \]

### Step 3: Calculate Selling Prices for the First Scenario
In the first scenario, the first bicycle is sold at a 10% profit and the second at a 20% profit.
- Selling price of the first bicycle (SP1) is:
\[ SP1 = A + 0.1A = 1.1A \]
- Selling price of the second bicycle (SP2) is:
\[ SP2 = B + 0.2B = 1.2B \]

### Step 4: Total Selling Price in the First Scenario
The total selling price in the first scenario is:
\[ SP1 + SP2 = 1.1A + 1.2B \]

### Step 5: Calculate Selling Prices for the Second Scenario
In the second scenario, the first bicycle is sold at a 20% profit and the second at a 10% profit.
- Selling price of the first bicycle (SP1') is:
\[ SP1' = A + 0.2A = 1.2A \]
- Selling price of the second bicycle (SP2') is:
\[ SP2' = B + 0.1B = 1.1B \]

### Step 6: Total Selling Price in the Second Scenario
The total selling price in the second scenario is:
\[ SP1' + SP2' = 1.2A + 1.1B \]

### Step 7: Set Up the Equation Based on the Problem Statement
According to the problem, the difference in selling prices between the two scenarios is Rs 5:
\[ (1.2A + 1.1B) - (1.1A + 1.2B) = 5 \]

### Step 8: Simplify the Equation
Simplifying the equation gives:
\[ 1.2A + 1.1B - 1.1A - 1.2B = 5 \]
\[ (1.2A - 1.1A) + (1.1B - 1.2B) = 5 \]
\[ 0.1A - 0.1B = 5 \]
Dividing the entire equation by 0.1:
\[ A - B = 50 \]

### Step 9: Solve the System of Equations
Now we have two equations:
1. \( A + B = 1600 \)
2. \( A - B = 50 \)

We can solve these equations simultaneously.

### Step 10: Add the Equations
Adding the two equations:
\[ (A + B) + (A - B) = 1600 + 50 \]
\[ 2A = 1650 \]
\[ A = 825 \]

### Step 11: Substitute to Find B
Now substitute \( A \) back into the first equation:
\[ 825 + B = 1600 \]
\[ B = 1600 - 825 \]
\[ B = 775 \]

### Step 12: Find the Difference
The difference of the cost price of the two bicycles is:
\[ A - B = 825 - 775 = 50 \]

### Final Answer
The difference of the cost price of the two bicycles is Rs 50.

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