A fruit seller had some oranges. He sold 80% of the oranges and still had 300 oranges left. How many oranges did he have initially?

Appeared in: DSSSB 6 September 2024

Explanation

The problem states that 80% of the oranges were sold. This means the remaining percentage is 100% - 80% = 20%.
We are given that the number of oranges left is 300, which corresponds to this 20% remainder.
To find the initial total (which represents 100%), we can set up the equation: 0.20 × Total = 300.
Solving for the total gives: Total = 300 / 0.20, which equals 1500.
Therefore, the fruit seller started with 1500 oranges.

Option B: If the initial total was 1350, the 20% of oranges remaining would be 0.20 × 1350 = 270, which does not match the 300 oranges left.
Option C: If the initial total was 2250, the 20% of oranges remaining would be 0.20 × 2250 = 450, which is not the 300 oranges stated in the problem.
Option D: This value is incorrect. If the total was 375, the 20% remaining would be only 75 oranges. This answer might result from incorrectly calculating 80% of 300 and adding it, or another logical error.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating an original value from a known percentage and the remaining quantity as background academic context rather than a clinical decision trigger.
Understanding percentages is a fundamental numeracy skill essential in nursing for tasks like calculating medication dosages, interpreting changes in patient weight, and understanding lab value shifts.
This type of 'find the whole' problem is analogous to clinical scenarios, such as calculating a patient's pre-illness weight based on a known percentage of weight loss.
What if? If the seller had sold 60% of the oranges and still had 300 left? In that case, the 300 oranges would represent 40% (100% - 60%) of the total. The initial amount would be 300 / 0.40 = 750 oranges.

How to Approach the Question

First, identify the key information given: the percentage of items sold (80%) and the actual number of items remaining (300).
Calculate the percentage that corresponds to the remaining items. If 80% were sold, the remaining percentage is 100% - 80% = 20%.
Recognize that this remaining percentage (20%) is equivalent to the remaining quantity (300).
Set up an equation to find the total (let's call it 'x'): 20% of x = 300, or 0.20 * x = 300.
Solve for 'x' by dividing the quantity by its corresponding percentage (in decimal form): x = 300 / 0.20.
Perform the calculation to find the initial total and select the matching option.

Concept Tested & Keywords

Concept Tested: Calculating an original value from a known percentage and the remaining quantity.
Stem keywords: fruit seller, oranges, sold 80%, 300 oranges left
Lead-in keywords: How many, initially

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Practise the full DSSSB 6 September 2024

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