A cycle dealer offers a discount of 10% and still makes a profit of 26%. What does he pay for a cycle whose marked price is Rs 840 ?

Options

A. Rs 600
B. Rs 650
C. Rs 700
D. Rs 750

Answer

To find out how much the cycle dealer paid for the cycle, we can use the relationship between the cost price (CP), marked price (MP), discount, and profit.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Marked Price (MP) = Rs 840
- Discount = 10%
- Profit = 26%

2. **Calculate the Selling Price (SP):**
The Selling Price after applying the discount can be calculated as follows:
\[ SP = MP - \text{Discount} \]
The discount amount is:
\[ \text{Discount} = \frac{10}{100} \times MP = \frac{10}{100} \times 840 = Rs 84 \]
Therefore, the Selling Price (SP) is:
\[ SP = 840 - 84 = Rs 756 \]

3. **Using the Profit Formula:**
The relationship between Cost Price (CP), Selling Price (SP), and Profit can be expressed as:
\[ SP = CP \times \left(1 + \frac{\text{Profit}}{100}\right) \]
Rearranging this formula to find the Cost Price (CP):
\[ CP = \frac{SP}{1 + \frac{\text{Profit}}{100}} \]

4. **Substituting the Values:**
Substitute the SP and Profit into the formula:
\[ CP = \frac{756}{1 + \frac{26}{100}} = \frac{756}{1.26} \]

5. **Calculating Cost Price (CP):**
Now, we calculate:
\[ CP = \frac{756}{1.26} \approx 600 \]

Thus, the cost price that the dealer paid for the cycle is Rs 600.

### Final Answer:
The dealer paid Rs 600 for the cycle.

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