Two numbers are respectively 30% and 40% more than a third number. In what ratio are these two numbers?

Appeared in: UPUMS Nsg officer-2023

Explanation

The problem requires finding the ratio between two numbers that are defined as percentage increases over a common base number.
Let the third number be 'x'. The first number is 1.30x (30% more) and the second number is 1.40x (40% more).
The ratio of the first number to the second is 1.30x : 1.40x.
The 'x' term cancels out, leaving the ratio 1.30 : 1.40.
To express this as a ratio of integers, multiply both sides by 10, which gives 13 : 14.

Option A: The ratio 10:11 would imply the numbers are related in that proportion, which does not align with increases of 30% and 40% from a common base.
Option B: The ratio 11:12 does not correspond to the calculated values of 130 and 140.
Option D: The ratio 12:13 is incorrect. It reverses the logic and does not match the calculated values.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Ratio and Percentage as background academic context rather than a clinical decision trigger.
This question assesses quantitative aptitude, a foundational skill for nurses.
Accurate mathematical calculation is critical in nursing for tasks such as medication dosage calculation, titrating IV drips, and interpreting patient data, where errors can have serious consequences.
What if? - If the numbers were 30% and 40% less than the third number, the first number would be 70 (100-30) and the second would be 60 (100-40). The ratio would be 70:60, which simplifies to 7:6.

How to Approach the Question

First, identify the core task: find the ratio between two numbers that are defined by their percentage increase over a common third number.
To simplify the calculations, assume the 'third number' is a convenient value like 100. This is a standard and effective strategy for percentage-based problems.
Calculate the value of the first number: 30% more than 100 is 100 + 30 = 130.
Calculate the value of the second number: 40% more than 100 is 100 + 40 = 140.
Formulate the ratio of the first number to the second number: 130:140.
Simplify this ratio by dividing both parts by their greatest common divisor (which is 10) to arrive at the final answer: 13:14.

Concept Tested & Keywords

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Practise the full UPUMS Nsg officer-2023

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