A dealer sold a bicycle at a profit of 10%. Had he bought the bicycle at 10% less price and sold it at a price Rs. 60 more, he would have gained 25%. The cost price of the bicycle was

Options

A. Rs2400
B. Rs2600
C. Rs2000
D. Rs2200

Answer

To solve the problem step by step, let's denote the cost price of the bicycle as \( CP \).

### Step 1: Understand the given information
The dealer sells the bicycle at a profit of 10%. This means the selling price (SP) can be expressed as:
\[ SP = CP + 0.1 \times CP = 1.1 \times CP \]

### Step 2: Calculate the new cost price
If the dealer had bought the bicycle at 10% less price, the new cost price would be:
\[ New\ CP = CP - 0.1 \times CP = 0.9 \times CP \]

### Step 3: Determine the new selling price
According to the problem, if he sold the bicycle for Rs. 60 more than the original selling price, the new selling price can be expressed as:
\[ New\ SP = SP + 60 = 1.1 \times CP + 60 \]

### Step 4: Set up the equation for the new profit
The problem states that with the new cost price and new selling price, he would have gained 25%. Therefore, the new selling price can also be expressed as:
\[ New\ SP = New\ CP + 0.25 \times New\ CP = 1.25 \times New\ CP \]
Substituting the new cost price:
\[ New\ SP = 1.25 \times (0.9 \times CP) = 1.125 \times CP \]

### Step 5: Equate the two expressions for New SP
Now we can set the two expressions for the new selling price equal to each other:
\[ 1.1 \times CP + 60 = 1.125 \times CP \]

### Step 6: Solve for CP
Rearranging the equation gives:
\[ 60 = 1.125 \times CP - 1.1 \times CP \]
\[ 60 = (1.125 - 1.1) \times CP \]
\[ 60 = 0.025 \times CP \]
Now, divide both sides by 0.025 to find \( CP \):
\[ CP = \frac{60}{0.025} = 2400 \]

### Conclusion
The cost price of the bicycle is Rs. 2400.

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