A trader presently earns 15 % profit by selling his product .If he increases the price of the product by Rs 24 , then his gain per cent increases to 27 % .Find the cost price of the product .

Options

A. Rs 20
B. Rs 200
C. Rs 150
D. Rs 160

Answer

To find the cost price of the product, we can follow these steps:

### Step 1: Define Variables
Let the cost price (CP) of the product be \( x \).

### Step 2: Calculate Initial Selling Price (SP)
The trader earns a profit of 15%. Therefore, the initial selling price (SP) can be calculated as:
\[ SP = CP + \text{Profit} = x + 0.15x = 1.15x \]

### Step 3: Calculate New Selling Price after Price Increase
If the trader increases the price of the product by Rs 24, the new selling price becomes:
\[ \text{New SP} = SP + 24 = 1.15x + 24 \]

### Step 4: Calculate New Gain Percentage
With the new selling price, the gain percentage increases to 27%. Thus, we can write the equation for the new selling price:
\[ \text{New Gain Percentage} = \frac{\text{New SP} - CP}{CP} \times 100 \]
Substituting the values we have:
\[ 27 = \frac{(1.15x + 24) - x}{x} \times 100 \]

### Step 5: Simplify the Equation
This simplifies to:
\[ 27 = \frac{0.15x + 24}{x} \times 100 \]
Dividing both sides by 100:
\[ 0.27 = \frac{0.15x + 24}{x} \]

### Step 6: Cross Multiply to Eliminate the Fraction
Cross multiplying gives:
\[ 0.27x = 0.15x + 24 \]

### Step 7: Rearrange the Equation
Rearranging the equation to isolate \( x \):
\[ 0.27x - 0.15x = 24 \]
\[ 0.12x = 24 \]

### Step 8: Solve for Cost Price (CP)
Now, divide both sides by 0.12:
\[ x = \frac{24}{0.12} = 200 \]

### Conclusion
Thus, the cost price of the product is:
\[ \text{Cost Price (CP)} = Rs 200 \]

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