The average weight of 60 students in a class is 40 kg. The average weight of boys is 50 kg and average weight of girls is 30 kg. The number of boys and girls respectively are equal to :

Question

Accepted Answer

To determine the number of boys and girls in the class, we need to use the information provided about the average weights and the total number of students. Let's break down the problem step by step:

1. **Total Students and Average Weight:**
   - Total number of students = 60
   - Average weight of all students = 40 kg

2. **Average Weights of Boys and Girls:**
   - Average weight of boys = 50 kg
   - Average weight of girls = 30 kg

3. **Equation Setup:**
   - Let the number of boys be $ b $ and the number of girls be $ g $.
   - We know that $ b + g = 60 $.

4. **Total Weight Calculation:**
   - Total weight of all students = 60 students × 40 kg/student = 2400 kg
   - Total weight of boys = $ b \times 50 $ kg
   - Total weight of girls = $ g \times 30 $ kg

5. **Equation for Total Weight:**
   - According to the problem, the total weight of boys and girls should equal the total weight of all students:
     $$
     b \times 50 + g \times 30 = 2400
     $$

6. **Substituting $ g = 60 - b $ into the Equation:**
   - Replace $ g $ with $ 60 - b $ in the total weight equation:
     $$
     b \times 50 + (60 - b) \times 30 = 2400
     $$
   - Simplify the equation:
     $$
     50b + 1800 - 30b = 2400
     $$
     $$
     20b + 1800 = 2400
     $$
     $$
     20b = 600
     $$
     $$
     b = 30
     $$

7. **Finding the Number of Girls:**
   - Since $ b = 30 $, and $ b + g = 60 $, we have:
     $$
     g = 60 - 30 = 30
     $$

8. **Conclusion:**
   - The number of boys is 30, and the number of girls is 30.

**Explanation of Incorrect Options:**

- **Option 1 (25, 35):** If there were 25 boys and 35 girls, the total weight would be $ 25 \times 50 + 35 \times 30 = 1250 + 1050 = 2300 $ kg, which does not match the required 2400 kg.
  
- **Option 2 (35, 25):** If there were 35 boys and 25 girls, the total weight would be $ 35 \times 50 + 25 \times 30 = 1750 + 750 = 2500 $ kg, which exceeds the required 2400 kg.
  
- **Option 3 (20, 40):** If there were 20 boys and 40 girls, the total weight would be $ 20 \times 50 + 40 \times 30 = 1000 + 1200 = 2200 $ kg, which is less than the required 2400 kg.

Therefore, Option 4 (30, 30) is the only correct answer that satisfies all the conditions given in the problem.