If a table sold for Rs. 437 at a loss of 8%, find its cost price. At what price must it be sold to gain 10%?

Answer

To solve the problem step by step, we will find the cost price (CP) of the table first, and then we will calculate the selling price (SP) required to achieve a gain of 10%.

### Step 1: Identify the given values
- Selling Price (SP) = Rs. 437
- Loss Percentage = 8%

### Step 2: Use the formula to find the Cost Price (CP)
The relationship between Cost Price (CP), Selling Price (SP), and Loss Percentage is given by the formula:
\[ CP = \frac{100 \times SP}{100 - \text{Loss Percentage}} \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ CP = \frac{100 \times 437}{100 - 8} \]
\[ CP = \frac{100 \times 437}{92} \]

### Step 4: Calculate the Cost Price
Now we will perform the calculation:
\[ CP = \frac{43700}{92} \]
Calculating this gives:
\[ CP = 475 \]
So, the Cost Price of the table is Rs. 475.

### Step 5: Find the Selling Price for a Gain of 10%
Next, we need to find the Selling Price (SP) that would give a gain of 10%. The formula for Selling Price when there is a gain is:
\[ SP = \frac{100 + \text{Gain Percentage}}{100} \times CP \]

### Step 6: Substitute the values into the formula
Substituting the known values into the formula:
\[ SP = \frac{100 + 10}{100} \times 475 \]
\[ SP = \frac{110}{100} \times 475 \]

### Step 7: Calculate the Selling Price
Now we will perform the calculation:
\[ SP = 1.1 \times 475 \]
Calculating this gives:
\[ SP = 522.5 \]
So, the Selling Price of the table to gain 10% is Rs. 522.5.

### Final Answers:
- Cost Price (CP) = Rs. 475
- Selling Price (SP) for 10% gain = Rs. 522.5