The ratio of number of girls to boys in a school of 4860 students is $53:55$. How many more girls should be admitted to make the ratio 1:1?

Appeared in: RRB Nsg. Superintendent-20 July 2019 (Shift-3rd)

Explanation

The total number of parts in the ratio is 53 (girls) + 55 (boys) = 108 parts.
The total student population of 4860 is divided by the 108 parts to find the value of one part: 4860 / 108 = 45 students.
The current number of boys is calculated as 55 parts × 45 students/part = 2475 boys.
The current number of girls is calculated as 53 parts × 45 students/part = 2385 girls.
To achieve a 1:1 ratio, the number of girls must be equal to the number of boys (2475).
The number of additional girls required is the difference between the number of boys and the current number of girls: 2475 - 2385 = 90.

Option A: This is an incorrect calculation. It does not represent the difference between the number of boys and girls.
Option B: This is an incorrect calculation. It may result from an error in calculating the number of students per ratio part or the final subtraction.
Option C: This is an incorrect calculation. It is close to the correct answer but likely arises from a minor arithmetic error.

Visual 1: Bar Chart - A bar chart could visually represent the initial numbers of girls (2385) and boys (2475), and then show the addition of 90 to the girls' bar to make both bars equal at 2475, illustrating the 1:1 ratio.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving word problems involving ratios and proportions as background academic context rather than a clinical decision trigger.
Ratio and proportion problems are a fundamental part of quantitative aptitude tests, which are common in various competitive examinations, including those for nursing positions.
This type of logical reasoning is applicable in healthcare for tasks like calculating medication dosages, interpreting lab value ratios, and managing staff-to-patient ratios.
What if? If the school wanted to achieve a 1:1 ratio by removing boys instead of adding girls, they would need to remove 90 boys. This would make the number of boys 2475 - 90 = 2385, which equals the number of girls.

How to Approach the Question

First, identify the key information provided: the total number of students (4860) and the initial ratio of girls to boys (53:55).
Sum the parts of the ratio to find the total number of parts: 53 + 55 = 108.
Divide the total number of students by the total ratio parts to determine the value of a single part: 4860 ÷ 108 = 45.
Calculate the current number of girls and boys by multiplying their respective ratio parts by the value of one part: Girls = 53 × 45 = 2385; Boys = 55 × 45 = 2475.
Understand the goal: a 1:1 ratio means the number of girls must equal the number of boys.
Since only girls are being added, the number of boys remains constant at 2475. Therefore, the target number of girls is also 2475.

Concept Tested & Keywords

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