A seller buys a watch for ₹ 2000 and marks it up to ₹ 3120. Further, he gives three successive discounts of `x%, y%` and `z%` in such a way that x + y + z = 37.5. If his overall profit/loss percentage is p, what could be the possible value of p?

Options

A. `62.5ltplt87.5`
B. `60ltplt62.5`
C. `-2.5ltplt4.5`
D. `60ltplt71.5`

Answer

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

### Step 1: Identify the Given Information
- Cost Price (CP) of the watch = ₹2000
- Marked Price (MP) of the watch = ₹3120
- Total discounts (x + y + z) = 37.5%

### Step 2: Calculate Selling Price (SP) with Discounts
The selling price after applying three successive discounts can be calculated using the formula:

\[ SP = MP \times \left(1 - \frac{x}{100}\right) \times \left(1 - \frac{y}{100}\right) \times \left(1 - \frac{z}{100}\right) \]

### Step 3: Consider the Minimum Selling Price
To find the minimum selling price, we can assume that two of the discounts (x and y) are 0, and z takes the entire discount of 37.5%. Thus:

\[ SP_{min} = 3120 \times \left(1 - \frac{37.5}{100}\right) \]

Calculating this:

\[ SP_{min} = 3120 \times 0.625 = 1950 \]

### Step 4: Calculate Loss Percentage for Minimum Selling Price
Now, we can calculate the loss incurred when the selling price is ₹1950:

\[ \text{Loss} = CP - SP_{min} = 2000 - 1950 = 50 \]

Loss percentage can be calculated as:

\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100 = \left(\frac{50}{2000}\right) \times 100 = 2.5\% \]

### Step 5: Consider the Maximum Selling Price
For the maximum selling price, we can assume that x, y, and z are equal. Therefore, each discount would be:

\[ x = y = z = \frac{37.5}{3} = 12.5\% \]

Now, calculate the selling price:

\[ SP_{max} = 3120 \times \left(1 - \frac{12.5}{100}\right)^3 \]

Calculating this:

\[ SP_{max} = 3120 \times 0.875^3 \]
\[ SP_{max} = 3120 \times 0.669921875 \approx 2093.5 \]

### Step 6: Calculate Gain Percentage for Maximum Selling Price
Now, we can calculate the gain incurred when the selling price is approximately ₹2093.5:

\[ \text{Gain} = SP_{max} - CP = 2093.5 - 2000 = 93.5 \]

Gain percentage can be calculated as:

\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{CP}\right) \times 100 = \left(\frac{93.5}{2000}\right) \times 100 \approx 4.675\% \]

### Step 7: Determine Overall Profit/Loss Percentage
From the calculations:
- Minimum loss percentage = 2.5%
- Maximum gain percentage = 4.675%

Thus, the overall profit/loss percentage (p) can range from:

\[ -2.5\% \text{ to } 4.675\% \]

### Final Answer
The possible value of p is between -2.5% and 4.5%, which corresponds to option C.

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