By selling a table for 350 instead of 400, loss per cent increases by 5%. The cost price of table is:

Options

A. 1050
B. 417.5
C. 435
D. 1000

Answer

To solve the problem step by step, we need to determine the cost price of the table based on the information provided.

### Step 1: Understand the given information
We know that the table is sold for Rs. 350 instead of Rs. 400, and the loss percentage increases by 5%.

### Step 2: Define variables
Let the cost price (CP) of the table be Rs. x.

### Step 3: Calculate the loss at both selling prices
1. **Selling Price (SP1)** = Rs. 400
- Loss when sold at SP1 = CP - SP1 = x - 400
- Loss Percentage when sold at SP1 = \(\frac{CP - SP1}{CP} \times 100 = \frac{x - 400}{x} \times 100\)

2. **Selling Price (SP2)** = Rs. 350
- Loss when sold at SP2 = CP - SP2 = x - 350
- Loss Percentage when sold at SP2 = \(\frac{CP - SP2}{CP} \times 100 = \frac{x - 350}{x} \times 100\)

### Step 4: Set up the equation based on the increase in loss percentage
According to the problem, the loss percentage increases by 5% when the selling price is reduced from Rs. 400 to Rs. 350. Therefore, we can write the equation as:

\[ \frac{x - 350}{x} \times 100 = \frac{x - 400}{x} \times 100 + 5 \]

### Step 5: Simplify the equation
1. Remove the percentage by dividing both sides by 100:
\[ \frac{x - 350}{x} = \frac{x - 400}{x} + \frac{5}{100} \]
\[ \frac{x - 350}{x} = \frac{x - 400}{x} + 0.05 \]

2. Multiply through by x to eliminate the denominator:
\[ x - 350 = x - 400 + 0.05x \]

3. Rearranging gives:
\[ x - 350 = x - 400 + 0.05x \]
\[ -350 + 400 = 0.05x \]
\[ 50 = 0.05x \]

### Step 6: Solve for x
Now, we can solve for x:
\[ x = \frac{50}{0.05} = 1000 \]

### Conclusion
The cost price of the table is Rs. 1000.