By selling 17 balls for Rs 720, a shopkeeper incurs a loss equal to the cost price of 5 balls. What is the cost price of one ball?

Introduction / Context:
This problem links total loss with the cost price of a certain number of items. Instead of giving a direct loss percentage, it states that the total loss is equal to the cost price of 5 balls. From the total selling price and this relation, we can determine the cost price per ball. This type of question trains you to translate verbal loss conditions into algebraic equations.

Given Data / Assumptions:

• Number of balls sold = 17.
• Total selling price for 17 balls = Rs 720.
• Total loss is equal to the cost price of 5 balls.
• We assume all balls have the same cost price.
• We must find cost price per ball.

Concept / Approach:
Let cost price of one ball be c. Then total cost price for 17 balls is 17c. Let total loss be L. The selling price is total cost - loss, i.e., SP = 17c - L. Given that L equals the cost of 5 balls, L = 5c. So SP = 17c - 5c = 12c. Setting this equal to 720 allows us to solve for c. This approach converts a word relation between loss and cost into a simple linear equation.

Step-by-Step Solution:
Step 1: Let cost price per ball = c.Step 2: Cost price of 17 balls = 17c.Step 3: Loss is equal to cost of 5 balls, so loss L = 5c.Step 4: Selling price of 17 balls SP = total CP - loss = 17c - 5c = 12c.Step 5: Given SP = Rs 720, so 12c = 720 ⇒ c = 720 / 12 = Rs 60.

Verification / Alternative check:
With c = Rs 60, total cost of 17 balls = 17 * 60 = Rs 1,020. Total loss is cost of 5 balls = 5 * 60 = Rs 300. Therefore, actual selling price = cost - loss = 1,020 - 300 = Rs 720, which matches the given selling price. This confirms that the cost price per ball is correctly found as Rs 60.

Why Other Options Are Wrong:
Rs 55, Rs 65 and Rs 70 do not satisfy the given relationship when used in the same equations. For example, if cost were Rs 55, total cost for 17 balls would be Rs 935 and losing 5 * 55 = Rs 275 would lead to SP = Rs 660, not Rs 720. Similar contradictions appear for Rs 65 and Rs 70. Only Rs 60 produces the correct total selling price of Rs 720 when the loss equals the cost of 5 balls.

Common Pitfalls:
Some students incorrectly assume that the loss equals 5/17 of the selling price instead of 5 times the cost price of one ball. Others try to compute a loss percentage first, which is unnecessary. The simplest method is to use a variable for cost price, set up the equation using the relation between loss and cost, and then solve directly for that variable.

Final Answer:
The cost price of each ball is Rs. 60.