70% of the cost price of a article Is equal to the 40% of its selling price. What is the profit or loss per cent ?

Options

A. 63%loss
B. 70%loss
C. 75%profit
D. 80%profit

Answer

To solve the problem step by step, we will start by translating the information given in the question into a mathematical equation.

### Step 1: Set up the equation
We know from the problem that:
- 70% of the Cost Price (CP) is equal to 40% of the Selling Price (SP).

This can be expressed mathematically as:
\[ 0.7 \times \text{CP} = 0.4 \times \text{SP} \]

### Step 2: Rearranging the equation
To eliminate the percentages, we can multiply both sides of the equation by 10 to make calculations easier:
\[ 7 \times \text{CP} = 4 \times \text{SP} \]

### Step 3: Express SP in terms of CP
Now, we can rearrange the equation to express the Selling Price (SP) in terms of the Cost Price (CP):
\[ \text{SP} = \frac{7}{4} \times \text{CP} \]

### Step 4: Calculate the profit
Now, we can find the profit. Profit is given by the formula:
\[ \text{Profit} = \text{SP} - \text{CP} \]

Substituting the expression for SP we found:
\[ \text{Profit} = \left(\frac{7}{4} \times \text{CP}\right) - \text{CP} \]
\[ \text{Profit} = \left(\frac{7}{4} - 1\right) \times \text{CP} \]
\[ \text{Profit} = \left(\frac{7}{4} - \frac{4}{4}\right) \times \text{CP} \]
\[ \text{Profit} = \frac{3}{4} \times \text{CP} \]

### Step 5: Calculate the profit percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100\% \]

Substituting the profit we calculated:
\[ \text{Profit Percentage} = \left(\frac{\frac{3}{4} \times \text{CP}}{\text{CP}}\right) \times 100\% \]
The CP cancels out:
\[ \text{Profit Percentage} = \frac{3}{4} \times 100\% \]
\[ \text{Profit Percentage} = 75\% \]

### Final Answer
The profit percentage is **75%**.

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