Question 54

The average of the marks of 30 boys is 88, and when the top two scores were excluded, the average marks reduced to 87.5. If the top two scores differ by 2, then the highest mark is:

Solution

Total marks of 30 boys = 88 $$\times 30 = 2640

($$\because$$ Average = sum of all term/number of terms)

when the top two scores were excluded, the average marks reduced to 87.5

Total marks of 28 boys = 87.5 $$\times 28 = 2450

Sum of the top two score = 2640 - 2450 = 190 ---(1)

difference of two score = 2

Let the top score be x so 2nd top score = x - 2

From eq(1),

x + x - 2 = 190

x = 192/2 = 96

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