Reena spent Rs 1200 on getting a table polished and then sold it for Rs 13,208 at `4%` gain. Find the cost price of the table.

Answer

To find the cost price of the table, we will follow these steps:

### Step 1: Understand the given information
- Selling Price (SP) = Rs 13,208
- Gain Percent = 4%
- Reena spent Rs 1200 on polishing the table.

### Step 2: Set up the equation for Cost Price (CP)
Let the cost price of the table be Rs x. The gain (profit) can be expressed as:
\[ \text{Gain} = \frac{\text{Gain Percent} \times \text{Cost Price}}{100} \]
Substituting the values we have:
\[ \text{Gain} = \frac{4 \times x}{100} = \frac{4x}{100} = \frac{x}{25} \]

### Step 3: Relate Selling Price, Cost Price, and Gain
The relationship between Selling Price, Cost Price, and Gain is given by:
\[ \text{Selling Price} = \text{Cost Price} + \text{Gain} \]
Substituting the values we have:
\[ 13208 = x + \frac{x}{25} \]

### Step 4: Combine the terms
To combine the terms, we need a common denominator. The common denominator for x and \(\frac{x}{25}\) is 25:
\[ 13208 = \frac{25x}{25} + \frac{x}{25} \]
\[ 13208 = \frac{25x + x}{25} \]
\[ 13208 = \frac{26x}{25} \]

### Step 5: Solve for x
Now, we can solve for x:
\[ 13208 \times 25 = 26x \]
\[ 330200 = 26x \]
\[ x = \frac{330200}{26} \]
\[ x = 12700 \]

### Step 6: Calculate the actual cost price
Since Reena spent Rs 1200 on polishing, the actual cost price of the table will be:
\[ \text{Actual Cost Price} = 12700 - 1200 \]
\[ \text{Actual Cost Price} = 11500 \]

### Final Answer
The actual cost price of the table is Rs 11,500.

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