Rohan sells his cycle to Mohan at 20% profit and Mohan spends Rs 400 on the repairing of cycle after that he sold it to Tina at 12.5% profit. If the cost price of cycle for Tina is Rs 4500, then find the cost price of cycle for Rohan?

Options

A. A)Rs 2500
B. B)Rs 3500
C. C)Rs 3000
D. D)Rs 4200

Answer

To find the cost price of the cycle for Rohan, we can follow these steps:

### Step 1: Define Variables
Let the cost price of the cycle for Rohan be \( X \).

### Step 2: Calculate Selling Price for Rohan
Rohan sells the cycle to Mohan at a profit of 20%.
The selling price (SP) can be calculated as:
\[ SP = CP + \text{Profit} = X + 0.20X = 1.20X \]
So, the selling price for Rohan is:
\[ SP_{Rohan} = 1.20X \]

### Step 3: Calculate Cost Price for Mohan
Mohan then spends Rs 400 on repairs. Therefore, the total cost price for Mohan becomes:
\[ CP_{Mohan} = SP_{Rohan} + \text{Repair Cost} = 1.20X + 400 \]

### Step 4: Calculate Selling Price for Mohan
Mohan sells the cycle to Tina at a profit of 12.5%.
The selling price for Mohan can be calculated as:
\[ SP_{Mohan} = CP_{Mohan} + \text{Profit} = CP_{Mohan} + 0.125 \times CP_{Mohan} = 1.125 \times CP_{Mohan} \]
Substituting the expression for \( CP_{Mohan} \):
\[ SP_{Mohan} = 1.125 \times (1.20X + 400) \]

### Step 5: Set Selling Price Equal to Tina's Cost Price
According to the problem, the cost price for Tina is Rs 4500. Therefore, we set the selling price for Mohan equal to 4500:
\[ 1.125 \times (1.20X + 400) = 4500 \]

### Step 6: Solve for \( X \)
Now, we can solve for \( X \):
1.125 times \( (1.20X + 400) = 4500 \)
\[ 1.20X + 400 = \frac{4500}{1.125} \]
Calculating \( \frac{4500}{1.125} \):
\[ \frac{4500}{1.125} = 4000 \]
So we have:
\[ 1.20X + 400 = 4000 \]
Subtracting 400 from both sides:
\[ 1.20X = 3600 \]
Dividing both sides by 1.20:
\[ X = \frac{3600}{1.20} = 3000 \]

### Conclusion
The cost price of the cycle for Rohan is Rs 3000.

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