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The average mark of 70 students in a class is 80. Out of these 70 stud

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Bunuel
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The average mark of 70 students in a class is 80. Out of these 70 stud [#permalink] New post   20 Feb 2019, 05:27
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The average mark of 70 students in a class is 80. Out of these 70 students, if the average mark of 40 students is 75, what is the average mark of the remaining 30 students rounded to the nearest integer?

A. 44
B. 58
C. 71
D. 86
E. 87
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kumarankit01
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Re: The average mark of 70 students in a class is 80. Out of these 70 stud [#permalink] New post   20 Feb 2019, 05:35
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Answer is E .

reduction in.marks by 40 = 40*5 ( difference between the total avg and the avg of these 40)

same reduction should be compensated by the rest 30 to have the avg of 80

so the 30 should have avg (80+ (200/30))
which gives 86.66
nearest one is 87.

award kudos if helpful.

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Re: The average mark of 70 students in a class is 80. Out of these 70 stud [#permalink] New post   20 Feb 2019, 08:47
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Bunuel wrote:
The average mark of 70 students in a class is 80. Out of these 70 students, if the average mark of 40 students is 75, what is the average mark of the remaining 30 students rounded to the nearest integer?

A. 44
B. 58
C. 71
D. 86
E. 87


total sum ; 80*70 = 5600
and score sum of 40 students = 3000
score sum of 30 students= 2600
avg . 87
IMO E
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Re: The average mark of 70 students in a class is 80. Out of these 70 stud [#permalink] New post   10 Oct 2021, 12:28
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Bunuel wrote:
The average mark of 70 students in a class is 80. Out of these 70 students, if the average mark of 40 students is 75, what is the average mark of the remaining 30 students rounded to the nearest integer?

A. 44
B. 58
C. 71
D. 86
E. 87


\(70*80 = 40*75 + 30*a\)

Or, \(5600 = 3000 + 30a\)

So, \(a = \frac{2600}{30}\)

Or, \(a = \frac{260}{3} = 86.67\) , Answer must be (E)
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Re: The average mark of 70 students in a class is 80. Out of these 70 stud [#permalink] New post   11 Oct 2021, 01:41
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Bunuel wrote:
The average mark of 70 students in a class is 80. Out of these 70 students, if the average mark of 40 students is 75, what is the average mark of the remaining 30 students rounded to the nearest integer?

A. 44
B. 58
C. 71
D. 86
E. 87


Solution:

We know \(average = \frac{sum of values}{total number of values}\). This means \(sum of values = average \times total number of values. \)

We are given the average mark of \(70\) students in a class is \(80\). This means the sum of marks if these 70 students \(= 80\times 70=5600\).

We are also given the average mark of \(40\) students is \(75\). This means the sum of marks if these 40 students \(= 40\times 75=3000\).

Thus sum of remaining 30 students \(= 5600-3000 = 2600\).

And average \(= \frac{2600}{30}=86.67=87\) (to nearest integer)

Hence the right answer is Option E.
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Re: The average mark of 70 students in a class is 80. Out of these 70 stud [#permalink] New post   19 Sep 2023, 12:59
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Re: The average mark of 70 students in a class is 80. Out of these 70 stud [#permalink]
19 Sep 2023, 12:59
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