While selling a watch a shopkeeper gives a discount of `5%`. If he gives a discount of `7%` he earns Rs. 15 less as profit, then the marked price of the watch is

Options

A. Rs. 697.50
B. Rs. 712.50
C. Rs. 787.50
D. Rs. 750

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Understand the Problem
The shopkeeper gives a discount of 5% on the marked price (MP) of a watch. If he gives a discount of 7%, he earns Rs. 15 less in profit. We need to find the marked price of the watch.

### Step 2: Define Variables
Let:
- MP = Marked Price of the watch
- CP = Cost Price of the watch
- SP1 = Selling Price when a 5% discount is given
- SP2 = Selling Price when a 7% discount is given

### Step 3: Express Selling Prices
The selling prices can be expressed as:
- SP1 = MP - 5% of MP = MP - 0.05 * MP = 0.95 * MP
- SP2 = MP - 7% of MP = MP - 0.07 * MP = 0.93 * MP

### Step 4: Express Profit
The profit when selling at SP1 and SP2 can be expressed as:
- Profit1 = SP1 - CP = 0.95 * MP - CP
- Profit2 = SP2 - CP = 0.93 * MP - CP

### Step 5: Set Up the Equation
According to the problem, the difference in profit between the two selling prices is Rs. 15:
Profit1 - Profit2 = 15
Substituting the profit expressions:
(0.95 * MP - CP) - (0.93 * MP - CP) = 15

### Step 6: Simplify the Equation
This simplifies to:
0.95 * MP - 0.93 * MP = 15
0.02 * MP = 15

### Step 7: Solve for MP
Now, divide both sides by 0.02:
MP = 15 / 0.02
MP = 750

### Conclusion
The marked price of the watch is Rs. 750.

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