A sold a cycle to B at a profit of 20%. B sold the cycle to at C at a profit of 30%. If C pays Rs 468 for Cycle, then for how much (in Rs) A bought the cycle?

Options

A. a)320
B. b)400
C. c)300
D. d)280

Answer

To find out how much A bought the cycle for, we can follow these steps:

### Step 1: Understand the Selling Prices
A sold the cycle to B at a profit of 20%. Let’s denote the cost price of the cycle for A as \( CP_A \).

### Step 2: Calculate Selling Price from A to B
If A bought the cycle for \( CP_A \), then the selling price from A to B can be calculated as:
\[ SP_{AB} = CP_A + 20\% \text{ of } CP_A = CP_A + 0.2 \times CP_A = 1.2 \times CP_A \]

### Step 3: Calculate Selling Price from B to C
B sold the cycle to C at a profit of 30%. The selling price from B to C can be calculated as:
\[ SP_{BC} = SP_{AB} + 30\% \text{ of } SP_{AB} = SP_{AB} + 0.3 \times SP_{AB} = 1.3 \times SP_{AB} \]

### Step 4: Substitute Selling Price from A to B
Now substituting \( SP_{AB} \) into the equation for \( SP_{BC} \):
\[ SP_{BC} = 1.3 \times (1.2 \times CP_A) = 1.56 \times CP_A \]

### Step 5: Set the Selling Price from B to C Equal to Rs 468
We know that C paid Rs 468 for the cycle, so we can set up the equation:
\[ 1.56 \times CP_A = 468 \]

### Step 6: Solve for \( CP_A \)
To find \( CP_A \), we divide both sides by 1.56:
\[ CP_A = \frac{468}{1.56} \]

### Step 7: Calculate \( CP_A \)
Now, performing the division:
\[ CP_A = 300 \]

Thus, A bought the cycle for Rs 300.

### Final Answer
A bought the cycle for Rs 300.

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