A cycle was sold at a loss of `8%`. If it was sold for Rs. 121 more, then there would have been a gain of `3%`. What was the cost price and selling price of the cycle respectively?

Options

A. Rs. 1012, Rs. 1000
B. Rs. 1000, Rs. 1300
C. Rs. 1100, Rs. 1012
D. Rs. 1002, Rs. 1100

Answer

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

### Step 1: Establish the equations based on the problem statement
1. The cycle was sold at a loss of 8%. This means:
\[ SP = CP - 0.08 \times CP = 0.92 \times CP \]

2. If the cycle was sold for Rs. 121 more, there would have been a gain of 3%. This means:
\[ SP + 121 = CP + 0.03 \times CP = 1.03 \times CP \]

### Step 2: Substitute the first equation into the second
From the first equation, we know:
\[ SP = 0.92 \times CP \]
Substituting this into the second equation gives:
\[ 0.92 \times CP + 121 = 1.03 \times CP \]

### Step 3: Rearrange the equation to isolate \( CP \)
Now, rearranging the equation:
\[ 121 = 1.03 \times CP - 0.92 \times CP \]
\[ 121 = (1.03 - 0.92) \times CP \]
\[ 121 = 0.11 \times CP \]

### Step 4: Solve for \( CP \)
Now, divide both sides by 0.11:
\[ CP = \frac{121}{0.11} = 1100 \]

### Step 5: Find the selling price \( SP \)
Now that we have \( CP \), we can find \( SP \):
\[ SP = 0.92 \times CP = 0.92 \times 1100 = 1012 \]

### Final Answer
The cost price and selling price of the cycle are:
- Cost Price (CP) = Rs. 1100
- Selling Price (SP) = Rs. 1012