If by selling 20 cycles Vinay incurs a loss equal to the selling price of 2 cycles, find his loss percentage.
A. `10%`
B. `11%`
C. `13 (1)/(3)%`
D. `9(1)/(11)%`

Options

A. B
B. D
C. A
D. C

Answer

To solve the problem, we need to find the loss percentage incurred by Vinay when selling 20 cycles. Here’s a step-by-step breakdown of the solution:

### Step 1: Define the Selling Price of One Cycle
Let the selling price (SP) of one cycle be denoted as \( SP = 1 \).

### Step 2: Calculate the Selling Price of 20 Cycles
The selling price of 20 cycles would then be:
\[ SP_{20} = 20 \times SP = 20 \times 1 = 20 \]

### Step 3: Understand the Loss
According to the problem, the loss incurred by Vinay is equal to the selling price of 2 cycles. Therefore, the loss (L) can be calculated as:
\[ L = SP_{2} = 2 \times SP = 2 \times 1 = 2 \]

### Step 4: Calculate the Cost Price
The cost price (CP) of the 20 cycles can be found using the formula:
\[ CP = SP + L \]
Substituting the values we have:
\[ CP = 20 + 2 = 22 \]

### Step 5: Calculate the Loss Percentage
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{L}{CP} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{2}{22} \right) \times 100 = \frac{200}{22} \approx 9.09\% \]

### Step 6: Simplify the Loss Percentage
To express \( \frac{200}{22} \) in a simpler form:
\[ \frac{200}{22} = \frac{100}{11} \approx 9.09\% \]
This can also be expressed as:
\[ 9 \frac{1}{11}\% \]

### Conclusion
Thus, the loss percentage incurred by Vinay is \( 9 \frac{1}{11}\% \).

### Final Answer
The correct option is **D. \( 9 \frac{1}{11}\% \)**.

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