On selling 18 balls for Rs. 900, there was a loss equal to the cost price of 6 balls. What is the cost price of one ball?

Options

A. Rs.5
B. Rs.75
C. Rs.70
D. Rs.80

Answer

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

### Step 1: Define the Variables
Let the cost price of one ball be \( x \).

### Step 2: Calculate the Cost Price of 18 Balls
The cost price of 18 balls will be:
\[ \text{Cost Price of 18 balls} = 18x \]

### Step 3: Determine the Loss
According to the problem, the loss incurred is equal to the cost price of 6 balls. Therefore, the loss can be expressed as:
\[ \text{Loss} = \text{Cost Price of 6 balls} = 6x \]

### Step 4: Calculate the Selling Price
The selling price of the 18 balls is given as Rs. 900.

### Step 5: Set Up the Loss Equation
The loss can also be calculated using the formula:
\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} \]
Substituting the known values:
\[ 6x = 18x - 900 \]

### Step 6: Rearrange the Equation
Rearranging the equation gives:
\[ 6x + 900 = 18x \]
\[ 900 = 18x - 6x \]
\[ 900 = 12x \]

### Step 7: Solve for \( x \)
Now, divide both sides by 12 to find \( x \):
\[ x = \frac{900}{12} = 75 \]

### Conclusion
The cost price of one ball is Rs. 75.

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