A machine is sold at a profit of `10%` Had it been sold for Rs. 40 less, there would have been a loss of `10%`. What was the cost price ?

Options

A. Rs. 175
B. Rs. 200
C. Rs. 225
D. Rs. 250

Answer

To find the cost price of the machine, we can follow these steps:

### Step 1: Define the Cost Price
Let the cost price (CP) of the machine be Rs. X.

### Step 2: Calculate Selling Price at 10% Profit
The selling price (SP) when sold at a profit of 10% can be calculated using the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where Profit = 10% of CP = \( \frac{10}{100} \times X = \frac{X}{10} \)

Thus, the selling price at 10% profit is:
\[ \text{SP} = X + \frac{X}{10} = \frac{10X}{10} + \frac{X}{10} = \frac{11X}{10} \]

### Step 3: Calculate Selling Price at 10% Loss
If the machine is sold for Rs. 40 less, the selling price becomes:
\[ \text{SP} = \frac{11X}{10} - 40 \]

When sold at a loss of 10%, the selling price can also be expressed as:
\[ \text{SP} = \text{CP} - \text{Loss} \]
Where Loss = 10% of CP = \( \frac{10}{100} \times X = \frac{X}{10} \)

Thus, the selling price at 10% loss is:
\[ \text{SP} = X - \frac{X}{10} = \frac{10X}{10} - \frac{X}{10} = \frac{9X}{10} \]

### Step 4: Set Up the Equation
According to the problem, both expressions for selling price are equal:
\[ \frac{11X}{10} - 40 = \frac{9X}{10} \]

### Step 5: Solve the Equation
Now, we can solve for X:
1. Rearranging the equation gives:
\[ \frac{11X}{10} - \frac{9X}{10} = 40 \]
\[ \frac{2X}{10} = 40 \]
\[ 2X = 400 \]
\[ X = 200 \]

### Conclusion
The cost price of the machine is Rs. 200.

---