An article is sold for Rs. 240 . If the profit is one-fourth of the cost price ,what is the cost price ?

Options

A. Rs. 180
B. Rs. 164
C. Rs. 192
D. Rs. 196

Answer

To find the cost price (CP) of the article, we can follow these steps:

### Step 1: Define the given values
- Selling Price (SP) = Rs. 240
- Profit = \( \frac{1}{4} \) of the Cost Price (CP)

### Step 2: Write the relationship between SP, CP, and Profit
The relationship can be expressed as:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Since the profit is \( \frac{1}{4} \) of CP, we can substitute this into the equation:
\[ \text{SP} = \text{CP} + \frac{1}{4} \text{CP} \]

### Step 3: Combine the terms
We can factor out CP from the right side:
\[ \text{SP} = \text{CP} \left(1 + \frac{1}{4}\right) \]
This simplifies to:
\[ \text{SP} = \text{CP} \left(\frac{4}{4} + \frac{1}{4}\right) \]
\[ \text{SP} = \text{CP} \left(\frac{5}{4}\right) \]

### Step 4: Substitute the value of SP
Now we can substitute the value of SP into the equation:
\[ 240 = \text{CP} \left(\frac{5}{4}\right) \]

### Step 5: Solve for CP
To isolate CP, we can multiply both sides by \( \frac{4}{5} \):
\[ \text{CP} = 240 \times \frac{4}{5} \]

### Step 6: Calculate the value
Now we can calculate:
\[ \text{CP} = 240 \times \frac{4}{5} = 240 \times 0.8 = 192 \]

Thus, the Cost Price (CP) is Rs. 192.

### Final Answer
The cost price of the article is Rs. 192.

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