A watch was sold at a profit of 15%. If its cost had been 5% less and it had been sold for 21 less, then the profit would have been 10%. Find the cost price of the watch

Options

A. Rs 400
B. Rs 190
C. Rs 200
D. None of these

Answer

To find the cost price of the watch, we will set up the problem using algebra. Let's denote the cost price of the watch as \( CP \).

### Step 1: Establish the Selling Price with 15% Profit
The selling price (SP) when the watch is sold at a profit of 15% can be calculated as:
\[ SP = CP + 0.15 \times CP = 1.15 \times CP \]

### Step 2: Establish the New Cost Price and Selling Price
According to the problem, if the cost price had been 5% less, the new cost price would be:
\[ New \, CP = CP - 0.05 \times CP = 0.95 \times CP \]
It is also stated that if the watch is sold for 21 less than the original selling price, the new selling price would be:
\[ New \, SP = SP - 21 = 1.15 \times CP - 21 \]

### Step 3: Establish the Profit with New Selling Price
With the new cost price, the profit is 10%. Therefore, we can express the new selling price in terms of the new cost price:
\[ New \, SP = New \, CP + 0.10 \times New \, CP = 1.10 \times New \, CP \]
Substituting the new cost price:
\[ New \, SP = 1.10 \times (0.95 \times CP) = 1.045 \times CP \]

### Step 4: Set Up the Equation
Now, we can set the two expressions for the new selling price equal to each other:
\[ 1.15 \times CP - 21 = 1.045 \times CP \]

### Step 5: Solve for CP
Rearranging the equation:
\[ 1.15 \times CP - 1.045 \times CP = 21 \]
\[ (1.15 - 1.045) \times CP = 21 \]
\[ 0.105 \times CP = 21 \]
Now, divide both sides by 0.105 to find \( CP \):
\[ CP = \frac{21}{0.105} = 200 \]

### Conclusion
Thus, the cost price of the watch is:
\[ \boxed{200} \]