If a watch is sold for र120, there is a loss of 15%. For a profit of 2%, the watch is to be sold for

Options

A. र 144
B. र 175
C. र 185
D. र 165

Answer

To solve the problem step by step, we need to first find the cost price of the watch and then determine the selling price required for a profit of 2%.

### Step 1: Identify the given values
- Selling Price (SP) = ₹120
- Loss Percentage = 15%

### Step 2: Use the formula for Selling Price with Loss
The formula for Selling Price when there is a loss is:
\[ SP = CP \times \left(1 - \frac{Loss \%}{100}\right) \]
Where CP is the Cost Price.

### Step 3: Substitute the known values into the formula
We can rearrange the formula to find the Cost Price (CP):
\[ 120 = CP \times \left(1 - \frac{15}{100}\right) \]
\[ 120 = CP \times \left(\frac{85}{100}\right) \]

### Step 4: Solve for Cost Price (CP)
Now, we can solve for CP:
\[ CP = \frac{120 \times 100}{85} \]
\[ CP = \frac{12000}{85} \]
\[ CP = 141.176 \text{ (approximately)} \]

### Step 5: Calculate the Selling Price for a Profit of 2%
Now that we have the Cost Price, we can find the Selling Price for a profit of 2%. The formula for Selling Price with profit is:
\[ SP = CP \times \left(1 + \frac{Profit \%}{100}\right) \]

### Step 6: Substitute the values into the profit formula
\[ SP = CP \times \left(1 + \frac{2}{100}\right) \]
\[ SP = 141.176 \times \left(\frac{102}{100}\right) \]

### Step 7: Calculate the Selling Price
\[ SP = 141.176 \times 1.02 \]
\[ SP = 144.00 \text{ (approximately)} \]

### Final Answer
The watch should be sold for approximately ₹144 to achieve a profit of 2%.

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