Two numbers are 40% and 60% respectively more than a third number. What is the ratio of the first number to the second number?

Appeared in: DSSSB - 29 August 2019 (Shift-1)

Explanation

Let the third number be 100 for simplicity in percentage calculations.
The first number is 40% more than 100, which is 100 + 40 = 140.
The second number is 60% more than 100, which is 100 + 60 = 160.
The ratio of the first number to the second number is 140:160.
Simplifying the ratio by dividing both sides by their greatest common divisor (20) gives 7:8.

Option A: This is the inverse of the correct ratio. It represents the ratio of the second number to the first number (160:140), not the first to the second.
Option B: This ratio (5:6) does not correspond to the relationship between 140 and 160. It may result from an arbitrary or incorrect calculation.
Option C: This is a common mistake made by taking the ratio of the percentages themselves (40:60) and simplifying it (4:6 -> 2:3). The calculation must be based on the numbers after the percentage increase is applied to the base number.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Ratios and Percentages as background academic context rather than a clinical decision trigger.
While this is a non-clinical question, proficiency in quantitative aptitude is essential for the General Intelligence and Reasoning sections of many nursing recruitment exams.
Strong numerical skills are fundamental for tasks like medication dosage calculation, interpreting lab results, and managing fluid balances, even though this specific problem is abstract.
What if the question asked for the ratio of the second number to the first? The calculation would be 160:140, which simplifies to 8:7 (Option A).

How to Approach the Question

Identify the base value in the problem, which is the 'third number'.
Assume a convenient value for the base, like 100, to make percentage calculations straightforward.
Calculate the values of the first and second numbers based on the given percentage increases. Remember that 'P% more than N' is N * (1 + P/100).
Formulate the ratio as requested in the question (First Number : Second Number).
Simplify the resulting ratio to its lowest terms by dividing both parts by their greatest common divisor.
Compare the simplified ratio with the given options to find the correct answer.

Concept Tested & Keywords

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Practise the full DSSSB - 29 August 2019 (Shift-1)

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