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The average marks of eight students in the Mathematics exam are 75. If the highest and lowest marks are removed, then the average marks become 80. If the ratio of the highest marks to the lowest marks is 3 : 1, then the highest marks are what percentage of the sum of the all the marks obtained by the eight students in the Mathematics exam?

The average marks of eight students in the Mathematics exam are 75. If the highest and lowest marks are removed, then the average marks become 80. If the ratio of the highest marks to the lowest marks is 3 : 1, then the highest marks are what percentage of the sum of the all the marks obtained by the eight students in the Mathematics exam? Correct Answer 15<span style="">%</span>

We know that,

Average = (Sum of Observations) ÷ (Total Numbers of Observations)

  • Sum of Observations = Average × Total Numbers of Observations

Given:

1) Average marks of eight students in the Mathematics exam are 75.

  • Sum of eight students mathematics marks = 75 × 8 = 600

2) If the highest and lowest marks are removed, then the average marks become 80.

  • Sum of six students mathematics marks = 80 × 6 = 480

3) The ratio of the highest marks to the lowest marks is 3 : 1.

Let the common factor of highest and lowest marks is x.

So highest number is 3x and lowest number is x.

From equation (1),

Sum of eight students mathematics marks = highest marks + lowers marks + Sum of six students mathematics marks

Putting the value from eq 1 and 2 and 3.

=> 600 = 3x + x + 480

=> 600 – 480 = 4x

=> 4x = 120

=> x = 30

So, highest number is = 3x = 3 × 30 = 90

The highest marks percentage of the sum of the all the marks obtained by the eight students is

=> (90 × 100) / 600 %

=> 9000 / 600 %

=> 15 %

Hence, the correct answer is “15 %”.

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