A school has 800 students with the ratio of boys to girls being 3:2. 400 new students were given admission and the ratio changed to 13:7. Find the number of boys who had taken admission.

1. A

   280

2. B

   320

3. C

   350

4. D

   300

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

Explanation

• First, calculate the initial number of boys: Total students (800) multiplied by the boys' fraction of the ratio (3/5) equals 480 boys.
• Next, calculate the total number of students after admission: 800 initial students + 400 new students = 1200 total students.
• Then, calculate the new number of boys based on the new ratio: New total students (1200) multiplied by the new boys' fraction (13/20) equals 780 boys.
• Finally, find the difference between the new number of boys and the initial number of boys: 780 - 480 = 300.
• The number of newly admitted girls can also be calculated to verify the answer: (Initial girls: 320, New girls: 420, Difference: 100). Total new students = 300 boys + 100 girls = 400.

Why Other Options Were Wrong

• Option A: If 280 boys were admitted, the total number of boys would become 480 + 280 = 760. The new ratio of boys to total students (1200) would be 760/1200, which simplifies to 19/30, not the required 13/20.
• Option B: If 320 boys were admitted, the total number of boys would be 480 + 320 = 800. The new ratio of boys to total students (1200) would be 800/1200, which simplifies to 2/3, not 13/20.
• Option C: If 350 boys were admitted, the total number of boys would be 480 + 350 = 830. The new ratio of boys to total students (1200) would be 830/1200 or 83/120. This does not match the final ratio of 13:7 (or 13/20 for boys).

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving problems involving ratios and proportions as background academic context rather than a clinical decision trigger.
• While this is a general aptitude question, the underlying mathematical principle of ratio and proportion is critical in nursing.
• Nurses frequently use ratio and proportion for drug dosage calculations to ensure patient safety. For example, calculating the correct volume of a medication to administer based on the prescribed dose and the concentration available (e.g., mg/mL).
• This skill is also used for calculating IV drip rates, preparing solutions of a specific concentration, and converting between different units of measurement.

How to Approach the Question

• First, identify the initial conditions: total number of people and the ratio between the subgroups.
• Calculate the absolute number for each subgroup in the initial condition. (Initial boys = 800 * 3/5).
• Next, identify the changes and the final conditions: the number of people added and the new ratio.
• Calculate the new total number of people and then use the new ratio to find the absolute number for each subgroup in the final condition. (New boys = 1200 * 13/20).
• Finally, subtract the initial number from the final number for the required subgroup to find the change. (New boys admitted = Final boys - Initial boys).

Concept Tested & Keywords

• Concept Tested: Solving problems involving ratios and proportions
• Stem keywords: ratio, boys to girls, students, admission
• Lead-in keywords: Find the number

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