I asked the shopkeeper the price of a wrist watch. I found that I had just the required sum of money. When the shopkeeper allowed me a discount of `25%`, I could bought another watch worth ₹ 940 for my younger sister. What is the price which I have paid for my own watch.?

Options

A. ₹ 2700
B. ₹ 1800
C. ₹ 2820
D. ₹ 3760

Answer

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

### Step 1: Understand the Discount
The shopkeeper offers a discount of 25%. This means that if the original price of the wristwatch is \( P \), the price after the discount is:
\[ \text{Discounted Price} = P - (25\% \text{ of } P) = P - 0.25P = 0.75P \]

### Step 2: Determine the Total Money Available
According to the problem, after getting the discount on the wristwatch, the remaining money allowed the person to buy another watch worth ₹940. Therefore, the total money the person had can be expressed as:
\[ \text{Total Money} = \text{Price of Own Watch after Discount} + 940 \]
Since the price of the own watch after discount is \( 0.75P \), we can write:
\[ \text{Total Money} = 0.75P + 940 \]

### Step 3: Equate Total Money with the Price of Own Watch
Since the total money the person had is equal to the price of the wristwatch before the discount, we can set up the equation:
\[ P = 0.75P + 940 \]

### Step 4: Solve for \( P \)
Rearranging the equation:
\[ P - 0.75P = 940 \]
\[ 0.25P = 940 \]
Now, divide both sides by 0.25 to find \( P \):
\[ P = \frac{940}{0.25} = 3760 \]

### Step 5: Calculate the Price Paid for Own Watch
Now that we have the original price \( P \), we can find the price paid for the own watch after the discount:
\[ \text{Price Paid} = 0.75P = 0.75 \times 3760 = 2820 \]

### Final Answer
The price which I have paid for my own watch is ₹2820.

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