A man sold an article at a gain of 5 %. A sold it for Rs. 240 more, he would have gained 8% more. Then the cost price of the article is

Options

A. a)12000
B. b)8000
C. c)6000
D. d)10000

Answer

To solve the problem step by step, we will denote the cost price (CP) of the article as \( x \).

### Step 1: Calculate the Selling Price (SP) at 5% Gain
The selling price when the article is sold at a gain of 5% can be calculated using the formula:
\[ SP = CP + \text{Gain} \]
Since the gain is 5% of the cost price, we can express this as:
\[ SP = x + \frac{5}{100} \times x = x + 0.05x = 1.05x \]

### Step 2: Calculate the Selling Price (SP) at 8% Gain
If the article is sold for Rs. 240 more, the new selling price will be:
\[ \text{New SP} = SP + 240 = 1.05x + 240 \]
At this new selling price, the gain is 8%, so we can express the new selling price as:
\[ \text{New SP} = x + \frac{8}{100} \times x = x + 0.08x = 1.08x \]

### Step 3: Set Up the Equation
Now, we can set the two expressions for the new selling price equal to each other:
\[ 1.05x + 240 = 1.08x \]

### Step 4: Solve for x
To find \( x \), we will rearrange the equation:
\[ 240 = 1.08x - 1.05x \]
\[ 240 = 0.03x \]
Now, divide both sides by 0.03:
\[ x = \frac{240}{0.03} = 8000 \]

### Conclusion
The cost price of the article is Rs. 8000.

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