The price of a bicycle is marked by a trader at Rs. 1000. He sold the bicycle allowing successive discounts of 20%, 10% ad 5%. Thus the trader gained 14% then the cost price of bicycle (in rupees) is :

Options

A. 790
B. 600
C. 560
D. 510

Answer

To solve the problem step by step, we need to calculate the selling price of the bicycle after applying the successive discounts and then find the cost price based on the given profit percentage.

### Step 1: Calculate the Selling Price after Discounts
The marked price of the bicycle is Rs. 1000. The trader allows successive discounts of 20%, 10%, and 5%.

1. **First Discount (20%)**:
- Discount Amount = 20% of 1000 = (20/100) * 1000 = Rs. 200
- Price after First Discount = 1000 - 200 = Rs. 800

2. **Second Discount (10%)**:
- Discount Amount = 10% of 800 = (10/100) * 800 = Rs. 80
- Price after Second Discount = 800 - 80 = Rs. 720

3. **Third Discount (5%)**:
- Discount Amount = 5% of 720 = (5/100) * 720 = Rs. 36
- Price after Third Discount = 720 - 36 = Rs. 684

So, the selling price after all discounts is Rs. 684.

### Step 2: Calculate the Cost Price
The trader gains a profit of 14%. This means the selling price is 114% of the cost price.

Let the cost price be \( CP \).

Using the formula for selling price:
\[ Selling Price = CP + Profit \]
\[ Selling Price = CP + 0.14 \cdot CP = 1.14 \cdot CP \]

From the selling price calculated:
\[ 684 = 1.14 \cdot CP \]

Now, we can solve for \( CP \):
\[ CP = \frac{684}{1.14} \]
\[ CP = 600 \]

### Conclusion
The cost price of the bicycle is Rs. 600.

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