A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had?

Appeared in: NCL (MP) Nursing Officer - 2019

Explanation

The problem states that 40% of the apples were sold, which means the percentage of apples remaining is 100% - 40% = 60%.
This remaining 60% of the total apples corresponds to the 420 apples the seller still has.
To find the original total (which is 100%), we can set up the equation: 0.60 × (Original Number of Apples) = 420.
Solving for the original number gives: 420 ÷ 0.60 = 700.
Therefore, the seller originally had 700 apples.

Option A: This answer (588) is the result of an incorrect calculation, likely by adding 40% of 420 to 420 (420 + 0.40*420 = 420 + 168 = 588). This wrongly assumes the 40% applies to the remaining apples, not the original total.
Option B: This is an incorrect guess. It might arise from a conceptual error, such as incorrectly assuming that 420 represents 70% of the total (420 / 0.7 = 600).
Option C: This answer (672) results from another miscalculation. It could be derived by adding 60% of 420 to 420 (420 + 0.60*420 = 420 + 252 = 672). This incorrectly applies the remaining percentage to the remaining quantity.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Percentage and Word Problems as background academic context rather than a clinical decision trigger.
Understanding how to calculate original values from percentages is a fundamental mathematical skill essential for data interpretation in various fields.
This type of reverse calculation is crucial for analyzing statistics, such as determining a baseline value when only a percentage change and a final value are known.
What if? If the seller sold 420 apples (which was 40% of the stock), how many would be left? In this case, the total is 420 / 0.40 = 1050. The remaining apples would be 1050 - 420 = 630.

How to Approach the Question

First, identify the key pieces of information: the percentage of items sold (40%) and the quantity of items remaining (420).
Determine the percentage of items remaining. If 40% are sold, the remainder is 100% - 40% = 60%.
Recognize that the quantity of remaining items (420) is equivalent to the percentage of remaining items (60%) of the original total.
Set up an equation to represent this relationship: Let 'X' be the original total. Then, 60% of X is 420, or 0.60 * X = 420.
Solve the equation for X by dividing the remaining quantity by the remaining percentage in decimal form: X = 420 / 0.60.
Calculate the final value and select the matching option.

Concept Tested & Keywords

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Practise the full NCL (MP) Nursing Officer - 2019

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