A man gives 30% of his oranges and is left with 140. How many did he have initially?

Appeared in: AIIMS CRE, SNO-2024

Explanation

The problem states that after giving away 30% of his oranges, a man is left with 140. This means the remaining 140 oranges represent 70% (100% - 30%) of the original total.
To find the initial total number of oranges (let's call it 'x'), we can set up a simple algebraic equation: 0.70 * x = 140.
By solving for 'x' (dividing 140 by 0.70), we find that x = 200. Therefore, the man originally had 200 oranges.

Option A: If the man started with 180 oranges, 70% of 180 is 126, not the 140 stated in the problem.
Option C: If the man started with 250 oranges, 70% of 250 is 175, not 140.
Option D: If the man started with 300 oranges, 70% of 300 is 210, not 140.

Visual 1: Infographic - A pie chart visually representing the problem. The chart would be divided into a 30% slice labeled 'Given Away' and a 70% slice labeled 'Remaining (140 oranges)', helping to visualize the relationship between the part and the whole.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving percentage-based word problems as background academic context rather than a clinical decision trigger.
Although a general math question, strong numeracy is a fundamental skill for nurses, crucial for patient safety.
Nurses constantly use similar calculations for medication dosages, IV fluid rates, and interpreting lab value changes, where precision is critical.
For instance, calculating a patient's weight loss percentage or titrating a drug infusion requires the same logical steps of understanding parts and wholes.

How to Approach the Question

First, identify the given information: a percentage given away (30%) and the remaining quantity (140).
Determine what the remaining quantity represents in terms of percentage. If 30% is gone, the remainder is 100% - 30% = 70%.
Translate the problem into a mathematical equation. Let 'X' be the initial total. The statement '70% of X is 140' becomes 0.70 * X = 140.
Solve the equation for 'X' by performing the inverse operation: X = 140 / 0.70.
Calculate the result (X = 200) and verify it. 30% of 200 is 60, and 200 - 60 = 140. The calculation is correct.

Concept Tested & Keywords

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Practise the full AIIMS CRE, SNO-2024

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