trader can procure 34 pencils by selling 28 pencils. What is the ratio of cost price to the selling price of a pencil

Options

A. 0.823529411764
B. 0.59513888888889
C. 0.37986111111111
D. 0.17152777777778

Answer

To solve the problem, we need to find the ratio of the cost price (CP) to the selling price (SP) of a pencil based on the information provided.

### Step-by-Step Solution:

1. **Understand the relationship between selling price and cost price:**
- The problem states that a trader can procure 34 pencils by selling 28 pencils. This means that the selling price of 28 pencils is equal to the cost price of 34 pencils.

2. **Let’s denote the selling price of 1 pencil:**
- Let the selling price of one pencil be \( SP \).
- Therefore, the selling price of 28 pencils is \( 28 \times SP \).

3. **Let’s denote the cost price of 1 pencil:**
- Let the cost price of one pencil be \( CP \).
- Therefore, the cost price of 34 pencils is \( 34 \times CP \).

4. **Set up the equation based on the relationship:**
- From the information given, we can write the equation:
\[ 28 \times SP = 34 \times CP \]

5. **Rearranging the equation to find the ratio of CP to SP:**
- We can rearrange the equation to find the ratio:
\[ \frac{CP}{SP} = \frac{28}{34} \]

6. **Simplifying the ratio:**
- Simplifying \( \frac{28}{34} \):
\[ \frac{28}{34} = \frac{14}{17} \]

7. **Final answer:**
- Therefore, the ratio of the cost price to the selling price of a pencil is:
\[ \frac{CP}{SP} = \frac{14}{17} \]