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In a class of 30 students, the average score in Mathematics is 75. If the averag

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Question: In a class of 30 students, the average score in Mathematics is 75. If the average score of the boys is 80 and that of the girls is 70, how many boys are there in the class? (2023)

Options:

  1. 10
  2. 15
  3. 20
  4. 25

Correct Answer: 15

Exam Year: 2023

Solution: 

Let the number of boys be x and the number of girls be 30 - x. The total score of boys is 80x and that of girls is 70(30 - x). The overall average is given by (80x + 70(30 - x)) / 30 = 75. Solving this gives x = 15.

In a class of 30 students, the average score in Mathematics is 75. If the averag

Practice Questions

Q1
In a class of 30 students, the average score in Mathematics is 75. If the average score of the boys is 80 and that of the girls is 70, how many boys are there in the class? (2023)
  1. 10
  2. 15
  3. 20
  4. 25

Questions & Step-by-Step Solutions

In a class of 30 students, the average score in Mathematics is 75. If the average score of the boys is 80 and that of the girls is 70, how many boys are there in the class? (2023)
  • Step 1: Understand that there are 30 students in total in the class.
  • Step 2: Let 'x' be the number of boys in the class.
  • Step 3: Since there are 30 students, the number of girls will be '30 - x'.
  • Step 4: The average score of the boys is 80, so the total score of the boys is 80 times the number of boys, which is 80x.
  • Step 5: The average score of the girls is 70, so the total score of the girls is 70 times the number of girls, which is 70(30 - x).
  • Step 6: The overall average score of the class is 75, which means the total score of all students divided by the number of students (30) equals 75.
  • Step 7: Write the equation for the overall average: (80x + 70(30 - x)) / 30 = 75.
  • Step 8: Multiply both sides of the equation by 30 to eliminate the fraction: 80x + 70(30 - x) = 75 * 30.
  • Step 9: Simplify the equation: 80x + 2100 - 70x = 2250.
  • Step 10: Combine like terms: 10x + 2100 = 2250.
  • Step 11: Subtract 2100 from both sides: 10x = 150.
  • Step 12: Divide both sides by 10 to find x: x = 15.
  • Step 13: Conclude that there are 15 boys in the class.
  • Averages – Understanding how to calculate and manipulate averages in a group.
  • Algebraic Equations – Setting up and solving equations based on given conditions.
  • Word Problems – Translating a real-world scenario into a mathematical model.
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