A table was sold at a profit of `10%` If its cost price was `5%` less and it was sold for Rs. 7 more the gain would have been `20%`. Find the cost price of the table.
A. Rs. 175
B. Rs. 200
C. Rs. 250
D. Rs. 150

Options

A. C
B. A
C. D
D. B

Answer

To solve the problem step by step, we will denote the cost price of the table as \( CP \).

### Step 1: Define the Cost Price
Let the cost price of the table be \( CP = 100k \).

### Step 2: Calculate Selling Price with 10% Profit
If the table is sold at a profit of 10%, the selling price \( SP \) can be calculated as:
\[ SP = CP + 10\% \text{ of } CP = 100k + 10\% \text{ of } 100k = 100k + 10k = 110k \]

### Step 3: New Cost Price and Selling Price
According to the problem, if the cost price was 5% less, the new cost price \( CP' \) would be:
\[ CP' = CP - 5\% \text{ of } CP = 100k - 5\% \text{ of } 100k = 100k - 5k = 95k \]

If it was sold for Rs. 7 more, the new selling price \( SP' \) would be:
\[ SP' = SP + 7 = 110k + 7 \]

### Step 4: Calculate New Selling Price with 20% Profit
The problem states that with the new cost price and selling price, the profit would be 20%. Therefore:
\[ SP' = CP' + 20\% \text{ of } CP' = 95k + 20\% \text{ of } 95k = 95k + 19k = 114k \]

### Step 5: Set Up the Equation
Now we have two expressions for \( SP' \):
1. \( SP' = 110k + 7 \)
2. \( SP' = 114k \)

Setting these equal to each other gives:
\[ 110k + 7 = 114k \]

### Step 6: Solve for \( k \)
Rearranging the equation:
\[ 114k - 110k = 7 \\ 4k = 7 \\ k = \frac{7}{4} \]

### Step 7: Find the Cost Price
Now, substituting \( k \) back to find the cost price \( CP \):
\[ CP = 100k = 100 \times \frac{7}{4} = 175 \]

Thus, the cost price of the table is Rs. 175.

### Final Answer
The cost price of the table is **Rs. 175**.