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

Options

A. Rs. 1050
B. Rs. 417.50
C. Rs. 435
D. Rs. 1000

Answer

To find the cost price of the table based on the information provided, we can follow these steps:

### Step 1: Understand the Selling Prices
The table was originally supposed to be sold for Rs. 400 but was sold for Rs. 350.

### Step 2: Calculate the Loss
The loss incurred when selling at Rs. 350 can be calculated as:
- Loss = Cost Price (CP) - Selling Price (SP)
- Loss = CP - 350

### Step 3: Determine the Increase in Loss Percentage
According to the problem, the loss percentage increases by 5% when the selling price changes from Rs. 400 to Rs. 350.

Let the original loss percentage when selling at Rs. 400 be \( x \% \). Therefore, the new loss percentage when selling at Rs. 350 is \( (x + 5) \% \).

### Step 4: Set Up the Equation for Loss Percentages
The loss when selling at Rs. 400 can be expressed as:
- Loss at Rs. 400 = CP - 400
- Loss Percentage at Rs. 400 = \(\frac{CP - 400}{CP} \times 100 = x\)

The loss when selling at Rs. 350 is:
- Loss at Rs. 350 = CP - 350
- Loss Percentage at Rs. 350 = \(\frac{CP - 350}{CP} \times 100 = x + 5\)

### Step 5: Write the Equations
From the above, we can write two equations:
1. \(\frac{CP - 400}{CP} \times 100 = x\)
2. \(\frac{CP - 350}{CP} \times 100 = x + 5\)

### Step 6: Solve the Equations
From equation 1, we can express \( x \):
\[ x = \frac{CP - 400}{CP} \times 100 \]

From equation 2, we can express \( x + 5 \):
\[ x + 5 = \frac{CP - 350}{CP} \times 100 \]

### Step 7: Substitute and Simplify
Substituting the value of \( x \) from the first equation into the second gives:
\[ \frac{CP - 400}{CP} \times 100 + 5 = \frac{CP - 350}{CP} \times 100 \]

### Step 8: Clear the Fractions
Multiply through by \( CP \) to eliminate the denominators:
\[ (CP - 400) \times 100 + 5CP = (CP - 350) \times 100 \]

### Step 9: Expand and Rearrange
Expanding both sides:
\[ 100CP - 40000 + 5CP = 100CP - 35000 \]
Combine like terms:
\[ -40000 + 5CP = -35000 \]
\[ 5CP = 5000 \]

### Step 10: Solve for Cost Price
Divide both sides by 5:
\[ CP = 1000 \]

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

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