By giving a discount of 10% on the marked price of Rs. 1100 of a cycle, a dealer galns 10%. The cost price of the cycle is :

Options

A. Rs. 1100
B. Rs. 900
C. Rs. 1089
D. Rs. 891

Answer

To solve the problem step by step, we will follow the information given in the question.

### Step 1: Identify the Marked Price and Discount
The marked price of the cycle is given as Rs. 1100, and the discount offered is 10%.

**Hint:** Remember that the marked price is the original price before any discounts are applied.

### Step 2: Calculate the Discount Amount
To find the discount amount, we calculate 10% of the marked price:
\[ \text{Discount} = \frac{10}{100} \times 1100 = 110 \]

**Hint:** To find a percentage of a value, multiply the percentage (as a fraction) by the total value.

### Step 3: Calculate the Selling Price
Now, we subtract the discount from the marked price to find the selling price:
\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} = 1100 - 110 = 990 \]

**Hint:** The selling price is what the customer pays after the discount is applied.

### Step 4: Understand the Gain Percentage
The dealer gains 10% on the cost price. If we let the cost price be \( CP \), then the selling price can be expressed in terms of the cost price:
\[ \text{Selling Price} = CP + 10\% \text{ of } CP = CP + \frac{10}{100} \times CP = 1.1 \times CP \]

**Hint:** A gain of 10% means the selling price is 110% of the cost price.

### Step 5: Set Up the Equation
From the previous step, we know the selling price is Rs. 990. Therefore, we can set up the equation:
\[ 990 = 1.1 \times CP \]

**Hint:** This equation allows us to find the cost price by isolating \( CP \).

### Step 6: Solve for the Cost Price
To find \( CP \), we divide both sides of the equation by 1.1:
\[ CP = \frac{990}{1.1} = 900 \]

**Hint:** When dividing by a decimal, it can be helpful to convert it to a fraction or multiply both the numerator and denominator by 10 to simplify.

### Conclusion
The cost price of the cycle is Rs. 900.

**Final Answer:** Rs. 900