Q13. In a class, the average weight of boys is 65 Kg and average weight of girls is 55 Kg. If average weight
of all students of the class is 62 Kg, find the number of girls in the class if boys are 35 in number.
1. 14
2.15
3. 12
4.20

How to Calculate the Number of Girls in a Class Based on Average Weight

Understanding how to calculate the number of girls in a class based on average weight is essential for solving competitive exam problems. This concept is commonly tested in exams like DBT BET JRF, CSIR NET Life Science, IIT JAM, and GATE Biotechnology. Let’s explore a practical example to understand how to solve such problems step-by-step.

Problem Statement

In a class, the average weight of boys is 65 kg, and the average weight of girls is 55 kg. If the average weight of all students in the class is 62 kg and the number of boys is 35, find the number of girls in the class.

Options:

1. 14
2. 15
3. 12
4. 20

Step-by-Step Solution

Step 1: Define the Variables

Let:

• Number of boys (B) = 35
• Average weight of boys = 65 kg
• Average weight of girls = 55 kg
• Average weight of all students = 62 kg
• Number of girls = G (to be calculated)

Step 2: Write the Equation for Total Weight

The total weight of boys =35×65=2275kg

The total weight of girls =  G×55

The total weight of all students = 2275+(G×55)

Step 3: Write the Equation for Average Weight

The average weight of all students is given by:

2275+(G×55)/ 35+G

=62

Step 4: Solve the Equation

Multiply both sides by (35 + G) to eliminate the fraction:

2275+(G×55) =62×(35+G) 

Expand the equation:

2275+55G=2170+62G

Rearrange terms:

2275−2170=62G−55G

105=7G

Divide both sides by 7:

G=15

Correct Answer:

The number of girls in the class is 15.
Option 2 is the correct answer.

Understanding the Concept

✅ Why This Problem is Important

• Problems involving average weight and mixture calculations are frequently tested in competitive exams.
• Knowing how to form equations and simplify them is essential for solving similar questions efficiently.

Formulas Used

1. Average weight of all students =

        Total weight of boys  + Total weight of girls​/ ​Number of Boys + Number of Girls 

2. Rearranging terms and simplifying the equation helps to isolate the unknown variable.

Importance for Competitive Exams

DBT BET JRF:

• Questions on averages, ratios, and algebraic simplifications are common.

CSIR NET Life Science:

• Data interpretation and mathematical reasoning are part of the exam pattern.

IIT JAM:

• Mathematical skills and logical reasoning are tested in the exam.

GATE Biotechnology:

• Problem-solving and analytical skills are essential to score high.

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Conclusion

Calculating the number of girls in a class based on average weight involves forming and solving algebraic equations. This type of question is frequently asked in competitive exams like DBT BET JRF, CSIR NET Life Science, IIT JAM, and GATE Biotechnology. With the right approach and structured preparation from Let’s Talk Academy, you can master this concept and improve your exam performance.