On selling 15 balls for Rs. 750, there is a loss equal to the cost of 3 balls. What is the cost price of 1 ball?

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

The problem states that the loss from selling 15 balls equals the cost price (C.P.) of 3 balls.
The basic formula for a transaction with a loss is: Selling Price (S.P.) = Cost Price (C.P.) - Loss.
Applying this to the entire transaction: S.P. of 15 balls = C.P. of 15 balls - C.P. of 3 balls.
This simplifies the relationship to: S.P. of 15 balls = C.P. of 12 balls.
Given that the S.P. of 15 balls is Rs. 750, we have: Rs. 750 = C.P. of 12 balls.
To find the C.P. of one ball, we divide the total cost by the number of balls: C.P. of 1 ball = Rs. 750 / 12 = Rs. 62.5.

Option A: This value is incorrect. It would be the answer if the loss was equal to the cost of 2.5 balls (S.P. = 15x - 2.5x = 12.5x; 750/12.5 = 60), which contradicts the problem statement.
Option C: This value represents the selling price per ball (750 / 15 = 50). The question asks for the cost price, which must be higher than the selling price because a loss was made.
Option D: This value is a result of a calculation error and does not correspond to a logical interpretation of the problem's conditions.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Profit and Loss Calculation as background academic context rather than a clinical decision trigger.
This is a general aptitude question testing mathematical skills, not a clinical concept.
Basic numeracy is an essential skill for nurses for tasks like medication dosage calculation, titrating drips, calculating intake/output, and interpreting patient data charts.
Accuracy in calculation is critical to ensure patient safety and effective treatment.

How to Approach the Question

First, identify the given values: Selling Price of 15 balls = Rs. 750.
Next, identify the key relationship provided: Loss = Cost Price of 3 balls.
Define a variable for the value you need to find. Let 'x' be the Cost Price (C.P.) of one ball.
Formulate the standard profit/loss equation. For a loss, it is: Selling Price = Cost Price - Loss.
Substitute the specific values from the problem into this equation: 750 = (15 * x) - (3 * x).
Simplify and solve the resulting algebraic equation for 'x': 750 = 12x, which gives x = 750 / 12.

Concept Tested & Keywords

Concept Tested: Profit and Loss Calculation
Stem keywords: selling 15 balls, Rs. 750, loss equal to the cost of 3 balls, cost price
Lead-in keywords: What is
Negative lead-in flag: false

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Practise the full DSSSB - 29 August 2019 (Shift-2)

Attempt every question from this paper in a timed mock, then review the full solution for each one.