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The average height of the girls of a class is 150 cm and the average height of the boys of the class is 5 cm more than the average of the class. If number of girls is 25% less than the number of boys what is the average height of the boys. 
  • a)
    161.66 cm 
  • b)
    160.5cm 
  • c)
    162.66 cm 
  • d)
    166.66 cm 
Correct answer is option 'A'. Can you explain this answer?
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The average height of the girls of a class is 150 cm and the average h...
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The average height of the girls of a class is 150 cm and the average h...
Given:
- Average height of girls = 150 cm
- Average height of boys = Average height of class + 5 cm
- Number of girls = 25% less than the number of boys

To find:
- Average height of boys

Solution:

Let's assume:
- Total number of students in the class = n
- Number of boys = x
- Number of girls = 0.75x (25% less than the number of boys)

Average height of the class
The average height of the class can be calculated by taking the weighted average of the average heights of boys and girls, where the weights are the respective proportions of boys and girls in the class.

Average height of class = (Average height of girls * Number of girls + Average height of boys * Number of boys) / Total number of students
Average height of class = (150 * 0.75x + (Average height of boys * x)) / n

Average height of boys
Since the average height of boys is 5 cm more than the average height of the class, we can write:
Average height of boys = Average height of class + 5 cm
Average height of boys = (150 * 0.75x + (Average height of boys * x)) / n + 5 cm

Simplifying the equation:
Average height of boys = (150 * 0.75x + Average height of boys * x + 5n) / n

Now we can solve this equation to find the value of Average height of boys.

Substituting the given values:
Average height of boys = (150 * 0.75x + Average height of boys * x + 5n) / n

Since the average height of boys is given as 5 cm more than the average height of the class, we can write:
Average height of boys = (150 * 0.75x + (Average height of class + 5) * x + 5n) / n

Average height of boys = (150 * 0.75x + (Average height of class * x + 5x + 5n) / n

We know that Average height of class = (150 * 0.75x + (Average height of boys * x)) / n

Therefore, Average height of boys = (150 * 0.75x + Average height of boys * x + 5x + 5n) / n

Simplifying the equation:
Average height of boys = (150 * 0.75 + x + 5n) / n

Calculating the values:
Since the average height of the boys is given as 5 cm more than the average height of the class, we can write:
Average height of boys = Average height of class + 5 cm

Substituting the values:
Average height of boys = 150 + 5
Average height of boys = 155 cm

Therefore, the average height of the boys is 155 cm.

Hence, option 'A' is the correct answer.
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