High School

There are 40 boys in a class. One of them weighing 100 kg goes away. A new boy joins the class at the same time. Consequently, the average weight of the boys is increased by 0.25 kg. Find the weight of the new boy.

Options:
1. 98.5
2. 110
3. 105
4. 99

Answer :

To find the weight of the new boy, let's work with the given data step by step using algebra and the concept of averages.


  1. Initial Setup:


    • Number of boys in the class = 40

    • Weight of the boy who leaves = 100 kg



  2. Effect of the Boy Leaving:


    • When the boy weighing 100 kg leaves, the total weight of the class decreases.


    • Let the initial average weight of the class be [tex]A[/tex] kg.


    • So, the total initial weight of the class is [tex]40A[/tex] kg.


    • The total weight after the boy leaves = [tex]40A - 100[/tex] kg.




  3. New Boy Joins:


    • A new boy joins, and now there are still 40 boys.

    • Let the weight of the new boy be [tex]x[/tex] kg.

    • The new total weight is [tex](40A - 100 + x)[/tex] kg.



  4. New Average Weight:


    • New average weight after the change = [tex]A + 0.25[/tex] kg.


    • Therefore, [tex]\frac{40A - 100 + x}{40} = A + 0.25[/tex]




  5. Solve for [tex]x[/tex]:


    • Multiply the entire equation by 40 to eliminate the fraction:
      [tex]40A - 100 + x = 40(A + 0.25)[/tex]


    • Distribute on the right side of the equation:
      [tex]40A - 100 + x = 40A + 10[/tex]


    • Simplify to find [tex]x[/tex]:
      [tex]x = 40A + 10 - (40A - 100)[/tex]
      [tex]x = 40A + 10 - 40A + 100[/tex]
      [tex]x = 110[/tex]




  6. Conclusion:

    Therefore, the weight of the new boy is 110 kg.

    Thus, the correct option is 2: 110.


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