The ratio of boys to girls in a class is 7 : 11. If 5 more boys joined the class, the ratio would change to 3 : 4. What was the initial number of students in the class?

1. A

   44

2. B

   54

3. C

   90

4. D

   72

Appeared in: NORCET 2 -2021 (Shift-2)

Explanation

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• The initial number of boys and girls can be represented as 7x and 11x, respectively, making the initial total number of students 18x.
• After 5 more boys join, the new number of boys is 7x + 5, and the number of girls is still 11x. The new ratio is (7x + 5) / 11x = 3/4.
• Solving this equation by cross-multiplication gives 4(7x + 5) = 3(11x), which simplifies to 28x + 20 = 33x.
• Further simplification leads to 5x = 20, which means x = 4.
• The initial total number of students is 18x. Substituting x = 4 gives 18 * 4 = 72.

Why Other Options Were Wrong

• Option A: This value represents the initial number of girls in the class (11x = 11 * 4 = 44), not the total number of students.
• Option B: This number does not correspond to any logical step or partial calculation in the problem. It is likely a result of a calculation error.
• Option C: This value would be the result if the variable 'x' was incorrectly calculated as 5 (18 * 5 = 90). This could happen from an arithmetic error when solving the equation, such as 20 / 4 instead of 20 / 5.

Related Visual

• Visual 1: Flowchart: A visual breakdown of the problem-solving steps, starting from defining variables for the initial ratio, setting up the equation based on the new condition, solving for the variable, and finally calculating the initial total number of students.

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 linear equations as background academic context rather than a clinical decision trigger.
• This question tests general aptitude and numerical ability, which is a component of many nursing entrance examinations.
• Strong analytical and problem-solving skills are essential for nurses for tasks like medication dosage calculations, interpreting lab results, and managing patient data.
• What if the question asked for the new total number of students? After finding x=4, the initial total is 72. Since 5 boys were added, the new total would be 72 + 5 = 77.

How to Approach the Question

• First, read the problem carefully to identify the initial ratio and the change that occurs.
• Represent the initial quantities using a common variable 'x' (e.g., Boys = 7x, Girls = 11x).
• Formulate an algebraic expression for the new quantities after the change (e.g., New Boys = 7x + 5).
• Set up an equation using the new ratio provided in the problem.
• Solve the linear equation to find the value of 'x'.
• Finally, use the value of 'x' to calculate the quantity the question asks for (in this case, the initial total number of students, 18x).

Concept Tested & Keywords

• Concept Tested: Solving word problems involving ratios and linear equations.
• Stem keywords: ratio, boys to girls, 7 : 11, 5 more boys, ratio would change, 3 : 4, initial number of students
• Lead-in keywords: What was

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