When 17 balls are sold for 720, the loss is equal to the cost price of 5 balls. find the C.P. of a ball:

Options

A. A) 60
B. B) 70
C. C) 80
D. D) 90

Answer

To find the cost price (C.P.) of a ball, let's break down the problem step by step.

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

### Step 2: Calculate the Total Cost Price
The total cost price for 17 balls will be:
\[ \text{C.P. of 17 balls} = 17x \]

### Step 3: Identify Selling Price
The selling price (S.P.) of the 17 balls is given as:
\[ \text{S.P.} = 720 \]

### Step 4: Understand Loss
The problem states that the loss is equal to the cost price of 5 balls. Therefore, the loss can be expressed as:
\[ \text{Loss} = \text{C.P. of 5 balls} = 5x \]

### Step 5: Relate Loss to C.P. and S.P.
The formula for loss is:
\[ \text{Loss} = \text{C.P.} - \text{S.P.} \]
Substituting the known values:
\[ 5x = 17x - 720 \]

### Step 6: Rearrange the Equation
Now, rearranging the equation gives:
\[ 5x + 720 = 17x \]
\[ 720 = 17x - 5x \]
\[ 720 = 12x \]

### Step 7: Solve for \( x \)
To find \( x \), divide both sides by 12:
\[ x = \frac{720}{12} \]
\[ x = 60 \]

### Step 8: Conclusion
The cost price of one ball is:
\[ \text{C.P. of one ball} = 60 \]

### Final Answer
The cost price of a ball is \( \text{Rs. } 60 \).

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