If the C.P. of `25` chairs is equal to the S.P. of `30` chairs, find the loss percent.

Options

A. loss `= "Rs. 5"`
loss percent `= 16 2/3 %`
B. loss `= "Rs. 8"`
loss percent `= 17 2/3 %`
C. loss `= "Rs. 9"`
loss percent `= 16 %`
D. loss `= "Rs. 12"`
loss percent `= 23 %`

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Cost Price (C.P.) of One Chair
Let the cost price of one chair be \( C.P. = 100x \).

### Step 2: Write the Equation Based on the Given Information
According to the question, the cost price of 25 chairs is equal to the selling price of 30 chairs. We can express this mathematically as:
\[ C.P. \text{ of } 25 \text{ chairs} = S.P. \text{ of } 30 \text{ chairs} \]
This can be written as:
\[ 25 \times C.P. = 30 \times S.P. \]

### Step 3: Substitute the Cost Price into the Equation
Substituting the expression for \( C.P. \):
\[ 25 \times (100x) = 30 \times S.P. \]
This simplifies to:
\[ 2500x = 30 \times S.P. \]

### Step 4: Solve for the Selling Price (S.P.)
Now, we can solve for \( S.P. \):
\[ S.P. = \frac{2500x}{30} = \frac{250x}{3}. \]

### Step 5: Calculate the Loss
The loss can be calculated using the formula:
\[ \text{Loss} = C.P. - S.P. \]
Substituting the values we have:
\[ \text{Loss} = 100x - \frac{250x}{3}. \]
To perform this subtraction, we need a common denominator:
\[ \text{Loss} = \frac{300x}{3} - \frac{250x}{3} = \frac{50x}{3}. \]

### Step 6: Calculate the Loss Percent
The loss percent is calculated using the formula:
\[ \text{Loss Percent} = \left( \frac{\text{Loss}}{C.P.} \right) \times 100. \]
Substituting the values:
\[ \text{Loss Percent} = \left( \frac{\frac{50x}{3}}{100x} \right) \times 100. \]
This simplifies to:
\[ \text{Loss Percent} = \left( \frac{50}{3 \times 100} \right) \times 100 = \frac{50}{3}. \]

### Step 7: Approximate the Loss Percent
Calculating \( \frac{50}{3} \) gives approximately \( 16.67\% \).

### Final Answer
The loss percent is approximately \( 16.67\% \).

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