In a college, the number of students studying Arts, Commerce and Science are in the ratio of 4 : 7 : 9. If the number of students in Arts, Commerce and Science be increased by 30%, 20% and 40% respectively, what will be the new ratio?

Appeared in: RRB Staff Nurse Jaipur-6th June 2018

Explanation

The core task is to adjust an initial ratio (4:7:9) based on individual percentage increases (30%, 20%, 40%) for each part.
To solve, assume initial numbers proportional to the ratio (e.g., 400, 700, 900) to make percentage calculations straightforward.
Calculate the new number for each stream: Arts becomes 400 * 1.3 = 520; Commerce becomes 700 * 1.2 = 840; Science becomes 900 * 1.4 = 1260.
The new, unsimplified ratio is 520 : 840 : 1260.
Simplify this ratio by dividing all parts by their greatest common divisor (20), which results in the final ratio of 26 : 42 : 63.

Option A: This ratio (24:40:64) results from incorrect simplification or calculation errors. For instance, simplifying 52:84:126 by an incorrect common factor might lead to a wrong answer.
Option B: This option (26:40:60) has the correct first term (26) but incorrect second and third terms. This indicates a calculation error in the Commerce and Science streams' increases.
Option D: This ratio (22:40:60) is entirely incorrect. None of the terms match the correctly calculated and simplified new ratio.

Visual 1: Flowchart illustrating the step-by-step process of calculating a new ratio from an initial ratio and given percentage increases.

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 tests quantitative aptitude, a fundamental skill for nurses used in various calculations like drug dosage, IV drip rates, and interpreting patient data trends.
Accurate calculation is critical for patient safety. A mistake in a real-world nursing calculation can have serious consequences.
What if the increase for Science was 50% instead of 40%? The new Science number would be 900 * 1.5 = 1350. The new ratio would be 520:840:1350, which simplifies to 52:84:135. This highlights how a single change affects the entire outcome.

How to Approach the Question

First, identify the initial ratio given in the problem (4 : 7 : 9).
To make calculations easier, assign placeholder numbers to each part of the ratio that are easy to work with for percentages, such as 400, 700, and 900.
Calculate the new value for each part by applying its specific percentage increase. The formula is: New Value = Initial Value × (1 + Percentage Increase / 100).
After calculating the new numbers for all parts (Arts, Commerce, Science), write them down as a new ratio.
Simplify this new ratio by finding the greatest common divisor (GCD) and dividing each number by it.
Compare your final, simplified ratio to the given options to find the correct answer.

Concept Tested & Keywords

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