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In a class of 88 students, the number of girls is 20% more than the number of boys. The average height of the boys is 164 cm, and the average height of girls is 4 cm less than the average height of all the boys and girls in the class. What is he average height (in cm) of all the students in the class?

In a class of 88 students, the number of girls is 20% more than the number of boys. The average height of the boys is 164 cm, and the average height of girls is 4 cm less than the average height of all the boys and girls in the class. What is he average height (in cm) of all the students in the class? Correct Answer 159.2

Given:

Total number of student = 88

The number of girls is 20% more than the number of boys.

The average height of the boys = 164 cm

The average height of girls is 4 cm less than the average height of all the boys and girls in the class.

Formula used:

Average = (Sum of total observations)/(total numbers of observation)

Calculation:

Let the number of boys be 'x'.

Again let the total average of the student be 'y'.

So, the average height of girls = y – 4

The number of girls =  20% more than the number of boys

⇒ The numbers of girls = x + 20% of x

⇒ x + (20x)/100

⇒ (6x/5)

According to the question,

Total numbers of student = 88

⇒ x + (6x/5) = 88

⇒ (11x/5) = 88

⇒ x = 40

So, the number of girls = 6x/5 = (6 × 40)/5 = 48

The number of boys = x = 40

(Sum of total observations) = Average × (total numbers of observation)

Sum of total height of student = y × 88 = 88y

Sum of total height of boys = 164 × 40 = 6560

Sum of total height of girls = (y – 4)  × 48 = 48y – 192

Sum of total height of student = sum of total height of boys and girl

⇒ 88y = 6560 + 48y – 192

⇒ 40y = 6368

⇒ y = 159.2 

∴ The average height of total student is 159.2.

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