If 30% 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 the linear equation: 0.30x + 50 = x, where 'x' is the unknown number.
To solve for 'x', the terms containing 'x' are grouped on one side: 50 = x - 0.30x.
This simplifies to 50 = 0.70x.
Dividing 50 by 0.70 gives the value of x, which is 500/7.

Option A: If the number is 50, then 30% of 50 is 15. Adding this to 50 gives 15 + 50 = 65, which is not equal to the original number, 50.
Option B: If the number is 100, then 30% of 100 is 30. Adding this to 50 gives 30 + 50 = 80, which is not equal to the original number, 100.
Option C: If the number is 150, then 30% of 150 is 45. Adding this to 50 gives 45 + 50 = 95, which is not equal to the original number, 150.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving linear equations involving percentages from word problems as background academic context rather than a clinical decision trigger.
Accurate calculation skills are fundamental in nursing for tasks like medication dosage calculation, IV drip rate adjustments, and interpreting lab results, where a small mathematical error can have significant patient safety consequences.
What if? - If the question was '30% of a number when subtracted from 50 is equal to the number', the equation would be 50 - 0.30x = x. Solving this gives 50 = 1.30x, so x = 50 / 1.3 = 500/13. This highlights how critical it is to correctly interpret the wording of a problem.

How to Approach the Question

First, identify the unknown value in the word problem and represent it with a variable, such as 'x'.
Carefully translate the phrases in the problem into mathematical expressions. For example, '30% of a number' becomes 0.30x.
Construct a complete equation by linking the expressions according to the problem statement. Here, it is 0.30x + 50 = x.
Use algebraic rules to solve the equation for the variable 'x'. The goal is to isolate 'x' on one side of the equation.
Once you find a value for 'x', substitute it back into the original word problem or equation to verify that it is the correct solution.

Concept Tested & Keywords

Concept Tested: Solving linear equations involving percentages from word problems.
Stem keywords: 30%, number, added to 50, equal to the number
Lead-in keywords: 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.