A sells a bicycle to B at a profit of 20% and B sells it to C at a profit of 25%. If C pays Rs 1500, what did A pay for it?

Options

A. Rs 825
B. Rs 1000
C. Rs 1100
D. Rs 1125

Answer

To solve the problem step by step, we will first determine how much A paid for the bicycle based on the selling prices and profit percentages.

### Step 1: Understand the selling prices and profits
- A sells the bicycle to B at a profit of 20%.
- B sells the bicycle to C at a profit of 25%.
- C pays Rs 1500 for the bicycle.

### Step 2: Calculate the selling price from B to C
Let’s denote the price at which A sells the bicycle to B as \( SP_{AB} \).

Since B sells it to C at a profit of 25%, we can express this as:
\[ SP_{BC} = SP_{AB} + 0.25 \times SP_{AB} = 1.25 \times SP_{AB} \]

### Step 3: Set up the equation with the known selling price
We know that C pays Rs 1500 for the bicycle:
\[ SP_{BC} = 1500 \]
Thus, we can set up the equation:
\[ 1.25 \times SP_{AB} = 1500 \]

### Step 4: Solve for \( SP_{AB} \)
To find \( SP_{AB} \), we divide both sides of the equation by 1.25:
\[ SP_{AB} = \frac{1500}{1.25} \]
\[ SP_{AB} = 1200 \]

### Step 5: Calculate the cost price for A
Now we know that A sells the bicycle to B for Rs 1200, and this is at a profit of 20%. We can express A's cost price \( CP_A \) as:
\[ SP_{AB} = CP_A + 0.20 \times CP_A = 1.20 \times CP_A \]

Now we can set up the equation:
\[ 1200 = 1.20 \times CP_A \]

### Step 6: Solve for \( CP_A \)
To find \( CP_A \), we divide both sides by 1.20:
\[ CP_A = \frac{1200}{1.20} \]
\[ CP_A = 1000 \]

### Conclusion
Thus, A paid Rs 1000 for the bicycle.