A watch when sold at a profit of 6% yields ₹870 more than when it is sold at a loss of 6%. Find the cost price of the watch.

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Define the Variables
Let the cost price of the watch be \( X \).

### Step 2: Calculate Selling Price at Profit
When the watch is sold at a profit of 6%, the selling price (SP1) can be calculated as:
\[ SP1 = X + 0.06X = 1.06X \]

### Step 3: Calculate Selling Price at Loss
When the watch is sold at a loss of 6%, the selling price (SP2) can be calculated as:
\[ SP2 = X - 0.06X = 0.94X \]

### Step 4: Set Up the Equation
According to the problem, the difference between the two selling prices is ₹870. Therefore, we can set up the equation:
\[ SP1 - SP2 = 870 \]
Substituting the values we calculated:
\[ 1.06X - 0.94X = 870 \]

### Step 5: Simplify the Equation
Now, simplify the left side of the equation:
\[ (1.06 - 0.94)X = 870 \]
\[ 0.12X = 870 \]

### Step 6: Solve for X
To find the cost price \( X \), divide both sides by 0.12:
\[ X = \frac{870}{0.12} \]

### Step 7: Calculate the Value
Now, perform the calculation:
\[ X = 870 \times \frac{100}{12} = 870 \times 8.33 = 7250 \]

### Conclusion
Thus, the cost price of the watch is:
\[ \text{Cost Price} = ₹7250 \]

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