If 50% of a number when added to 50 is equal to the number. Then the number is:

Appeared in: SGPGI Nursing Officer-2024

Explanation

The problem is translated into a linear equation. Let the unknown number be 'x'.
The statement '50% of a number when added to 50 is equal to the number' is written as: 0.5x + 50 = x.
To solve for x, first isolate the variable. Subtract 0.5x from both sides of the equation, which results in 50 = 0.5x.
Finally, divide 50 by 0.5 to find the value of x, which is 100.

Option A: If the number were 50, then 50% of 50 is 25. Adding 50 to 25 gives 75, which is not equal to the original number 50.
Option C: If the number were 150, then 50% of 150 is 75. Adding 50 to 75 gives 125, which is not equal to the original number 150.
Option D: If the number were 75, then 50% of 75 is 37.5. Adding 50 to 37.5 gives 87.5, which is not equal to the original number 75.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a linear equation derived from a word problem involving percentages as background academic context rather than a clinical decision trigger.
While not a clinical question, strong mathematical skills are essential for safe nursing practice.
Nurses frequently use algebra for tasks like calculating medication dosages, determining IV fluid rates, and converting between different units of measurement.
A mistake in calculation can have serious consequences for patient safety.

How to Approach the Question

First, read the problem carefully to understand what is being asked. Identify the unknown value and assign it a variable, like 'x'.
Translate the words into a mathematical equation. Break down each phrase: '50% of a number' becomes 0.5x, 'added to 50' becomes + 50, and 'is equal to the number' becomes = x.
Assemble the full equation: 0.5x + 50 = x.
Solve the equation for the variable 'x' using standard algebraic steps, such as combining like terms and isolating the variable.
After finding a value for 'x', substitute it back into the original word problem to verify that it makes the statement true.
Select the option that matches your calculated result.

Concept Tested & Keywords

Concept Tested: Solving a linear equation derived from a word problem involving percentages.
Stem keywords: 50%, added to 50, equal to the number
Lead-in keywords: Then the number is

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Practise the full SGPGI Nursing Officer-2024

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