A number exceeds 30% of itself by 49. The number is ?

Appeared in: HPSSC - 2015

Explanation

The problem can be translated into the algebraic equation: x - (30/100) * x = 49.
Simplifying the equation gives x - 0.30x = 49, which further simplifies to 0.70x = 49.
Solving for x involves dividing 49 by 0.70.
The calculation yields x = 49 / 0.70, which equals 70.
Verification confirms the answer: 30% of 70 is 21, and 70 - 21 = 49.

Option A: If the number is 56, then 30% of 56 is 16.8. The difference is 56 - 16.8 = 39.2, which is not 49.
Option B: If the number is 63, then 30% of 63 is 18.9. The difference is 63 - 18.9 = 44.1, which is not 49.
Option D: If the number is 210, then 30% of 210 is 63. The difference is 210 - 63 = 147, which is not 49. This error might come from misinterpreting the relationship between the numbers.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving algebraic word problems involving percentages as background academic context rather than a clinical decision trigger.
While not a clinical scenario, this question assesses fundamental numeracy skills, which are critical in nursing.
Nurses frequently use percentage calculations for tasks such as determining medication dosages, calculating IV fluid rates, and interpreting changes in a patient's weight or lab values.
A strong grasp of these mathematical concepts is essential for patient safety and effective care.

How to Approach the Question

First, carefully read the problem to understand what is being asked. Identify the unknown quantity and assign it a variable, such as 'x'.
Translate the words of the problem into a mathematical equation. 'A number (x) exceeds (=) 30% of itself (0.30x) by 49' translates to x - 0.30x = 49.
Simplify the algebraic equation. Combine the terms with the variable 'x' (1x - 0.30x = 0.70x).
Solve the simplified equation (0.70x = 49) for the variable 'x' by performing the necessary arithmetic operations (x = 49 / 0.70).
After finding the value of x, substitute it back into the original problem statement to verify that it is the correct solution.

Concept Tested & Keywords

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Practise the full HPSSC - 2015

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