On selling 17 balls at ₹ 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is (S.S.C., 2004)

### Concept & Logic Loss occurs when the Cost Price is greater than the Selling Price. We can express this relationship mathematically using the quantities given in the problem. $$ \text{Loss} = \text{Total CP} - \text{Total SP} $$ ### Step-by-Step Solution 1. Let the Cost Price (CP) of 1 ball be denoted as CP. 2. The loss on selling 17 balls is equal to the CP of 5 balls. 3. According to the loss formula: Loss = CP of 17 balls - SP of 17 balls. 4. Substitute the given loss: CP of 5 balls = CP of 17 balls - SP of 17 balls. 5. Rearrange the equation to solve for SP: $$ \text{SP of 17 balls} = \text{CP of 17 balls} - \text{CP of 5 balls} $$ $$ \text{SP of 17 balls} = \text{CP of 12 balls} $$ 6. We are given that the SP of 17 balls is ₹ 720. 7. Therefore, the CP of 12 balls is also ₹ 720. 8. To find the CP of 1 ball, divide the total CP by the number of balls: $$ \text{CP of 1 ball} = 720 / 12 $$ 9. Calculate: $720 / 12 = 60$. ### Exam Strategy & Shortcut Translate directly: $\text{Loss} = \text{CP}_{17} - \text{SP}_{17}$. Since Loss = $\text{CP}_5$, then $\text{CP}_5 = \text{CP}_{17} - \text{SP}_{17}$. This rearranges to $\text{SP}_{17} = \text{CP}_{12}$. Given $\text{SP}_{17} = 720$, then $12 \times \text{CP} = 720 \Rightarrow \text{CP} = 60$. ### Common Pitfall A standard error is adding the 5 to the 17 instead of subtracting. Since it is a loss measured in CP, the selling price represents the value of fewer balls ($17 - 5 = 12$) than were actually sold. ### Final Answer Therefore, the correct answer is **₹ 60**.