If the cost price of `12` pencils is equal to the selling price of `15` pencils then find the loss% is

Options

A. `20%`
B. `25%`
C. `3%`
D. `16 2/3%`

Answer

To solve the problem step by step, we need to find the cost price (CP) and selling price (SP) of the pencils and then calculate the loss percentage.

**Step 1: Define the variables.**
Let the cost price of 12 pencils be denoted as CP(12) and the selling price of 15 pencils be denoted as SP(15).

**Step 2: Set up the equation based on the problem statement.**
According to the problem, the cost price of 12 pencils is equal to the selling price of 15 pencils:
\[ CP(12) = SP(15) \]

**Step 3: Express CP and SP in terms of the price per pencil.**
Let the cost price of one pencil be \( CP \) and the selling price of one pencil be \( SP \).
Then, we can express:
\[ CP(12) = 12 \times CP \]
\[ SP(15) = 15 \times SP \]

**Step 4: Substitute the expressions into the equation.**
From the earlier equation:
\[ 12 \times CP = 15 \times SP \]

**Step 5: Rearrange the equation to find the relationship between CP and SP.**
Rearranging gives us:
\[ \frac{CP}{SP} = \frac{15}{12} \]
This simplifies to:
\[ \frac{CP}{SP} = \frac{5}{4} \]

**Step 6: Calculate the loss.**
Loss occurs when the selling price is less than the cost price. The loss can be calculated as:
\[ \text{Loss} = CP - SP \]
Using the relationship we found:
Let \( SP = 4x \) (for some value \( x \)), then:
\[ CP = 5x \]
Thus:
\[ \text{Loss} = 5x - 4x = x \]

**Step 7: Calculate the loss percentage.**
Loss percentage is calculated using the formula:
\[ \text{Loss \%} = \left( \frac{\text{Loss}}{CP} \right) \times 100 \]
Substituting the values we found:
\[ \text{Loss \%} = \left( \frac{x}{5x} \right) \times 100 = \left( \frac{1}{5} \right) \times 100 = 20\% \]

**Final Answer:**
The loss percentage is **20%**.

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