In case of a particular transaction, the profit earned is `14(2)/7` %. What fraction is the cost price of the selling price?

Options

A. `1/7`
B. `8/7`
C. `7/8`
D. `1/8`

Answer

To solve the problem, we need to find the fraction of the cost price (CP) with respect to the selling price (SP) given that the profit percentage is \(14 \frac{2}{7}\%\).

### Step 1: Convert the mixed fraction to an improper fraction
The profit percentage is given as \(14 \frac{2}{7}\%\). To convert this to an improper fraction:
\[ 14 \frac{2}{7} = \frac{14 \times 7 + 2}{7} = \frac{98 + 2}{7} = \frac{100}{7} \]
So, the profit percentage is \(\frac{100}{7}\%\).

**Hint:** To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place it over the original denominator.

### Step 2: Convert the profit percentage to a fraction
To express the profit percentage as a fraction, we divide by 100:
\[ \text{Profit fraction} = \frac{100}{7} \times \frac{1}{100} = \frac{1}{7} \]

**Hint:** To convert a percentage to a fraction, divide the percentage by 100.

### Step 3: Relate profit to cost price and selling price
The profit can also be expressed in terms of cost price (CP) and selling price (SP):
\[ \text{Profit} = \text{SP} - \text{CP} \]
Using the profit fraction:
\[ \frac{1}{7} = \frac{\text{SP} - \text{CP}}{\text{CP}} \]

**Hint:** Remember that profit is the difference between selling price and cost price.

### Step 4: Rearranging the equation
Rearranging the equation gives:
\[ \text{SP} - \text{CP} = \frac{1}{7} \text{CP} \]
This can be rewritten as:
\[ \text{SP} = \text{CP} + \frac{1}{7} \text{CP} = \frac{7}{7} \text{CP} + \frac{1}{7} \text{CP} = \frac{8}{7} \text{CP} \]

**Hint:** When combining fractions, make sure they have a common denominator.

### Step 5: Finding the fraction of cost price to selling price
Now, we can express the cost price in terms of selling price:
\[ \frac{\text{CP}}{\text{SP}} = \frac{\text{CP}}{\frac{8}{7} \text{CP}} = \frac{1}{\frac{8}{7}} = \frac{7}{8} \]

**Hint:** To find the fraction of one quantity to another, divide the first quantity by the second.

### Final Answer
The fraction of the cost price with respect to the selling price is \(\frac{7}{8}\).