A man had a table to sell. I offered him a sum of money for the table which he refused as being 13% below the value of the table. I then offered Rs 450 more and the second offer was 5% more than the estimated value. Find the value of the table.

Answer

To find the value of the table, we can follow these steps:

### Step 1: Define the Variables
Let the estimated value of the table be \( CP \) (Cost Price).

### Step 2: Calculate the First Offer
The first offer made was 13% below the value of the table. Therefore, the first offer can be expressed as:
\[ \text{First Offer} = CP - 0.13 \times CP = 0.87 \times CP \]

### Step 3: Calculate the Second Offer
The second offer was Rs. 450 more than the first offer. Thus, we can express the second offer as:
\[ \text{Second Offer} = 0.87 \times CP + 450 \]

### Step 4: Set Up the Equation for the Second Offer
The second offer is also stated to be 5% more than the estimated value of the table. Therefore, we can express this as:
\[ \text{Second Offer} = CP + 0.05 \times CP = 1.05 \times CP \]

### Step 5: Equate the Two Expressions for the Second Offer
Now we can set the two expressions for the second offer equal to each other:
\[ 0.87 \times CP + 450 = 1.05 \times CP \]

### Step 6: Solve for \( CP \)
Rearranging the equation gives:
\[ 450 = 1.05 \times CP - 0.87 \times CP \]
\[ 450 = (1.05 - 0.87) \times CP \]
\[ 450 = 0.18 \times CP \]

Now, solving for \( CP \):
\[ CP = \frac{450}{0.18} \]
\[ CP = 2500 \]

### Conclusion
The value of the table is Rs. 2500.

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