5% more is gained by selling a watch for Rs. 350 than by sell ing it for Rs. 340. The cost price of the watch is

Options

A. Rs.10
B. Rs.140
C. Rs.200
D. Rs.250

Answer

To find the cost price (CP) of the watch based on the information provided, we can follow these steps:

### Step 1: Understand the given information
We know that selling the watch for Rs. 350 gives a profit that is 5% more than selling it for Rs. 340.

### Step 2: Define the variables
Let the cost price of the watch be \( X \).

### Step 3: Calculate the profit from selling at Rs. 340
When the watch is sold for Rs. 340, the profit can be expressed as:
\[ \text{Profit at Rs. 340} = 340 - X \]

### Step 4: Calculate the profit from selling at Rs. 350
When the watch is sold for Rs. 350, the profit can be expressed as:
\[ \text{Profit at Rs. 350} = 350 - X \]

### Step 5: Set up the equation based on the profit difference
According to the problem, the profit from selling at Rs. 350 is 5% more than the profit from selling at Rs. 340. Therefore, we can set up the equation:
\[ 350 - X = (340 - X) + 0.05 \times (340 - X) \]

### Step 6: Simplify the equation
First, calculate \( 0.05 \times (340 - X) \):
\[ 0.05 \times (340 - X) = \frac{340 - X}{20} \]
Now substitute this back into the equation:
\[ 350 - X = (340 - X) + \frac{340 - X}{20} \]

### Step 7: Combine like terms
To simplify, multiply everything by 20 to eliminate the fraction:
\[ 20(350 - X) = 20(340 - X) + (340 - X) \]
This gives:
\[ 7000 - 20X = 6800 - 20X + 340 - X \]
Combine like terms:
\[ 7000 - 20X = 6800 + 340 - 20X - X \]
This simplifies to:
\[ 7000 = 6800 + 340 - X \]
\[ 7000 = 7140 - X \]

### Step 8: Solve for \( X \)
Rearranging gives:
\[ X = 7140 - 7000 \]
\[ X = 140 \]

### Conclusion
The cost price of the watch is Rs. 140.