A person bought two bicycles for ₹ 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 ₹ 5 more.The difference in the cost price of the two bicycles was

Options

A. ₹ 25
B. ₹ 75
C. ₹ 50
D. ₹ 40

Answer

To solve the problem step by step, we will denote the cost price of the first bicycle as \( x \) and the cost price of the second bicycle as \( 1600 - x \) (since the total cost price of both bicycles is ₹1600).

### Step 1: Define the Cost Prices
Let:
- Cost Price of the first bicycle = \( x \)
- Cost Price of the second bicycle = \( 1600 - x \)

### Step 2: 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) = \( x + 0.1x = 1.1x \)
- Selling Price of the second bicycle (SP2) = \( (1600 - x) + 0.2(1600 - x) = 1.2(1600 - x) = 1920 - 1.2x \)

### Step 3: Calculate Total Selling Price for the First Scenario
Total Selling Price in the first scenario:
\[ SP_{total1} = SP1 + SP2 = 1.1x + (1920 - 1.2x) = 1920 - 0.1x \]

### Step 4: 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') = \( x + 0.2x = 1.2x \)
- Selling Price of the second bicycle (SP2') = \( (1600 - x) + 0.1(1600 - x) = 1.1(1600 - x) = 1760 - 1.1x \)

### Step 5: Calculate Total Selling Price for the Second Scenario
Total Selling Price in the second scenario:
\[ SP_{total2} = SP1' + SP2' = 1.2x + (1760 - 1.1x) = 1760 + 0.1x \]

### Step 6: Set Up the Equation Based on the Given Condition
According to the problem, the difference in selling prices between the two scenarios is ₹5:
\[ SP_{total2} - SP_{total1} = 5 \]
Substituting the expressions we derived:
\[ (1760 + 0.1x) - (1920 - 0.1x) = 5 \]

### Step 7: Simplify the Equation
Now, simplify the equation:
\[ 1760 + 0.1x - 1920 + 0.1x = 5 \]
Combining like terms:
\[ -160 + 0.2x = 5 \]

### Step 8: Solve for \( x \)
Rearranging the equation gives:
\[ 0.2x = 5 + 160 \]
\[ 0.2x = 165 \]
\[ x = \frac{165}{0.2} = 825 \]

### Step 9: Find the Cost Price of the Second Bicycle
Now, we can find the cost price of the second bicycle:
\[ \text{Cost Price of the second bicycle} = 1600 - x = 1600 - 825 = 775 \]

### Step 10: Calculate the Difference in Cost Prices
Finally, the difference in cost prices of the two bicycles is:
\[ \text{Difference} = 825 - 775 = 50 \]

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

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