A person sold an electronic watch at ₹ 96 in such a way that his percentage profit is same as the cost price of the watch. If he sells it at twice the percentage profit of its previous percentage profit, then the new selling price will be:

Options

A. ₹ 132
B. ₹ 150
C. ₹ 192
D. ₹ 180

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define Variables
Let the cost price (CP) of the watch be \( x \). According to the problem, the percentage profit is equal to the cost price, which means the percentage profit is also \( x \% \).

### Step 2: Set Up the Selling Price Equation
The selling price (SP) can be calculated using the formula:
\[ SP = CP + \text{Profit} \]
The profit can be expressed as:
\[ \text{Profit} = \frac{x}{100} \times CP = \frac{x}{100} \times x = \frac{x^2}{100} \]
Thus, the selling price becomes:
\[ SP = x + \frac{x^2}{100} \]
Given that the selling price is ₹96, we can set up the equation:
\[ x + \frac{x^2}{100} = 96 \]

### Step 3: Multiply Through by 100 to Eliminate the Fraction
To eliminate the fraction, multiply the entire equation by 100:
\[ 100x + x^2 = 9600 \]
Rearranging gives:
\[ x^2 + 100x - 9600 = 0 \]

### Step 4: Solve the Quadratic Equation
Now we will solve the quadratic equation using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \( a = 1 \), \( b = 100 \), and \( c = -9600 \):
\[ x = \frac{-100 \pm \sqrt{100^2 - 4 \cdot 1 \cdot (-9600)}}{2 \cdot 1} \]
Calculating the discriminant:
\[ 100^2 + 38400 = 10000 + 38400 = 48400 \]
Now, taking the square root:
\[ \sqrt{48400} = 220 \]
Substituting back into the formula:
\[ x = \frac{-100 \pm 220}{2} \]
Calculating the two possible values:
1. \( x = \frac{120}{2} = 60 \)
2. \( x = \frac{-320}{2} = -160 \) (not valid since cost price cannot be negative)

Thus, the cost price \( x = 60 \).

### Step 5: Calculate the Percentage Profit
Since the percentage profit is equal to the cost price, the percentage profit is \( 60\% \).

### Step 6: Calculate the New Selling Price
The new selling price will be calculated at twice the previous percentage profit:
\[ \text{New Percentage Profit} = 2 \times 60\% = 120\% \]
Now we calculate the new selling price:
\[ \text{New SP} = CP + \text{New Profit} \]
The new profit can be calculated as:
\[ \text{New Profit} = \frac{120}{100} \times 60 = 72 \]
Thus, the new selling price becomes:
\[ \text{New SP} = 60 + 72 = 132 \]

### Final Answer
The new selling price of the watch will be ₹132.

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