Some lollipopse are bought at 11 for a rupee and the same number at 9 a rupee if the whole lot is sold at 10 a rupee find the gain or loss per cent

Options

A. 2% gain
B. 2% loss
C. 1 % gain
D. 1 % loss

Answer

To solve the problem step by step, we will first determine the cost price of the lollipops bought at two different rates, and then calculate the selling price to find the gain or loss percentage.

### Step 1: Determine the number of lollipops bought
Let's assume we buy 990 lollipops of each kind.

### Step 2: Calculate the cost price of the first kind of lollipops
The first kind of lollipops is bought at 11 for a rupee. Therefore, the cost price (CP) for 990 lollipops is calculated as follows:
\[ \text{Cost Price of first kind} = \frac{990}{11} = 90 \text{ rupees} \]

### Step 3: Calculate the cost price of the second kind of lollipops
The second kind of lollipops is bought at 9 for a rupee. Therefore, the cost price for 990 lollipops is calculated as follows:
\[ \text{Cost Price of second kind} = \frac{990}{9} = 110 \text{ rupees} \]

### Step 4: Calculate the total cost price
Now, we add the cost prices of both kinds of lollipops:
\[ \text{Total Cost Price} = 90 + 110 = 200 \text{ rupees} \]

### Step 5: Calculate the selling price of the lollipops
The whole lot of lollipops is sold at 10 for a rupee. Therefore, the selling price (SP) for 990 lollipops is calculated as follows:
\[ \text{Selling Price} = \frac{990}{10} = 99 \text{ rupees} \]

### Step 6: Determine the gain or loss
Now, we can determine if there is a gain or loss by subtracting the total cost price from the selling price:
\[ \text{Loss} = \text{Total Cost Price} - \text{Selling Price} = 200 - 99 = 101 \text{ rupees} \]

### Step 7: Calculate the loss percentage
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{\text{Total Cost Price}}\right) \times 100 = \left(\frac{101}{200}\right) \times 100 = 50.5\% \]

### Final Answer
The loss percentage is **50.5%**.

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