Ramesh bought 10 cycles for Rs. 500 each. He spent Rs. 2,000 on the repair of all cycles. He sold five of them for Rs. 750 each and the remaining for Rs. 550 each. Then the total gain or loss % is

Options

A. Gain of `8(1)/(3)%`
B. Loss of `8(1)/(3)%`
C. Gain of `7(2)/(3)%`
D. Loss of `7(1)/(7)%`

Answer

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

### Step 1: Calculate the Total Cost Price (CP)
Ramesh bought 10 cycles for Rs. 500 each.

\[ \text{Total CP} = \text{Number of cycles} \times \text{Cost per cycle} = 10 \times 500 = 5000 \text{ Rs.} \]

He also spent Rs. 2000 on repairs.

\[ \text{Total CP (including repairs)} = \text{Total CP} + \text{Repair cost} = 5000 + 2000 = 7000 \text{ Rs.} \]

### Step 2: Calculate the Total Selling Price (SP)
Ramesh sold 5 cycles for Rs. 750 each.

\[ \text{SP for first 5 cycles} = 5 \times 750 = 3750 \text{ Rs.} \]

He sold the remaining 5 cycles for Rs. 550 each.

\[ \text{SP for remaining 5 cycles} = 5 \times 550 = 2750 \text{ Rs.} \]

Now, we calculate the total SP.

\[ \text{Total SP} = \text{SP for first 5 cycles} + \text{SP for remaining 5 cycles} = 3750 + 2750 = 6500 \text{ Rs.} \]

### Step 3: Determine Gain or Loss
Now we will find out whether there is a gain or loss by comparing the total SP with the total CP.

\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 7000 - 6500 = 500 \text{ Rs.} \]

### Step 4: Calculate Loss Percentage
To find the loss percentage, we use the formula:

\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]

Substituting the values:

\[ \text{Loss Percentage} = \left( \frac{500}{7000} \right) \times 100 \approx 7.14\% \]

### Final Answer
The total loss percentage is approximately **7.14%**.

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