Some toffees were bought at the rate of 11 for 10 and the same number at the rate of 9 for 10. If the whole lot was sold at one rupee per toffee, then the gain or loss in the whole transaction was

Options

A. loss of 1%
B. 1%gain of
C. neither gain nor loss
D. 1.5%gain of

Answer

To solve the problem step by step, we will calculate the cost price (CP) and selling price (SP) of the toffees, and then determine the gain or loss.

### Step 1: Determine the number of toffees bought
Let's assume we buy 99 toffees at each rate for easier calculations.

- **First Purchase:**
- Rate: 11 toffees for 10 rupees
- Number of toffees bought = 99
- Cost Price (CP) for 99 toffees = (99/11) * 10 = 90 rupees

- **Second Purchase:**
- Rate: 9 toffees for 10 rupees
- Number of toffees bought = 99
- Cost Price (CP) for 99 toffees = (99/9) * 10 = 110 rupees

### Step 2: Calculate the total cost price (CP)
Total CP = CP from first purchase + CP from second purchase
Total CP = 90 + 110 = 200 rupees

### Step 3: Calculate the total selling price (SP)
- Total number of toffees = 99 (from first purchase) + 99 (from second purchase) = 198 toffees
- Selling Price (SP) = 1 rupee per toffee
- Total SP = 198 toffees * 1 rupee/toffee = 198 rupees

### Step 4: Determine gain or loss
- Loss = Total CP - Total SP
- Loss = 200 - 198 = 2 rupees

### Step 5: Calculate the percentage loss
Percentage Loss = (Loss / Total CP) * 100
Percentage Loss = (2 / 200) * 100 = 1%

### Final Answer:
The loss in the whole transaction is 1%.

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