A 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. `2:3`
B. `14:17`
C. `9:7`
D. `4:7`

Answer

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

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

### Step 2: Define the cost price and selling price
Let:
- Cost Price (CP) of 28 pencils = 28 (since the trader sells 28 pencils)
- Selling Price (SP) of 34 pencils = 34 (since the trader can buy 34 pencils with the money from selling 28 pencils)

### Step 3: Calculate the cost price and selling price per pencil
To find the cost price and selling price per pencil, we divide the total cost price and selling price by the number of pencils:
- Cost Price per pencil = CP of 28 pencils / 28 = 28 / 28 = 1
- Selling Price per pencil = SP of 34 pencils / 34 = 34 / 34 = 1

### Step 4: Find the ratio of cost price to selling price
Now, we can find the ratio of cost price to selling price:
- Ratio (CP:SP) = Cost Price per pencil : Selling Price per pencil = 1 : 1

### Step 5: Simplify the ratio
Since both values are equal, the ratio can be simplified:
- The ratio of cost price to selling price = 1 : 1

### Final Answer
The ratio of cost price to selling price of a pencil is 1:1.

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