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# The average height of 40 students in a class is 172 cm. 30 students wh

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Math Expert
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The average height of 40 students in a class is 172 cm. 30 students wh  [#permalink]

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20 Feb 2019, 05:11
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45% (medium)

Question Stats:

70% (02:10) correct 30% (02:40) wrong based on 23 sessions

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The average height of 40 students in a class is 172 cm. 30 students whose average height is 172.5 cm left the class and 40 students whose average height is 170.5 cm joined the class. Find the average height of the present class.

A. 170 cm
B. 170.2 cm
C. 170.5 cm
D. 175
E. 177 cm

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Re: The average height of 40 students in a class is 172 cm. 30 students wh  [#permalink]

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20 Feb 2019, 05:29
Average height of 40 students in a class is 172 cm
$$\frac{Σ40}{40}$$=172 => Σ40= 6880.......................(1)

30 students whose average height is 172.5 cm leave the class
$$\frac{Σ30}{30}$$=172.5 => Σ30= 5175.......................(2)

(1)-(2) will give Σ10= 1705.............(3)

40 students whose average height is 170.5 cm join the class
$$\frac{Σ40}{40}$$=170.5 => Σ40= 6820.......................(4)

The average height of the present class will be the average of 50 students.
Σ50=(3)+(4)=1705+6820=8525

Thus, $$\frac{Σ50}{50}$$=$$\frac{8525}{50}$$=170.5
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Re: The average height of 40 students in a class is 172 cm. 30 students wh  [#permalink]

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20 Feb 2019, 09:51
Bunuel wrote:
The average height of 40 students in a class is 172 cm. 30 students whose average height is 172.5 cm left the class and 40 students whose average height is 170.5 cm joined the class. Find the average height of the present class.

A. 170 cm
B. 170.2 cm
C. 170.5 cm
D. 175
E. 177 cm

sum of 40 students ; 172 * 40 ; 6880
and of 30 students who left class; 172.5 * 30; 5175
now left with 10 students in class and weight of class; 6880-5175; 1705
the weight of 40 new students; 40 * 170.5 ; 6820
so new total of 50 students; 6820 + 1705 ; 8525
avg ; 8525/50 ; 170.5 IMO C
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Re: The average height of 40 students in a class is 172 cm. 30 students wh  [#permalink]

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20 Feb 2019, 10:30
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1
Bunuel wrote:
The average height of 40 students in a class is 172 cm. 30 students whose average height is 172.5 cm left the class and 40 students whose average height is 170.5 cm joined the class. Find the average height of the present class.

A. 170 cm
B. 170.2 cm
C. 170.5 cm
D. 175
E. 177 cm

Simply use the concept of aves discussed here to reduce calculations:

Avg of 40 students is 172 cm
30 students leave whose avg is 172.5 cm. So these 30 students had .5 cm extra i.e. total 15 extra.
When 15 cm is taken away from 10 students, this means 1.5 cm is taken away from each student so average goes down to 170.5 cm.

Now when 40 students with an average of 170.5 cm join, the average remains 170.5 cm.

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Re: The average height of 40 students in a class is 172 cm. 30 students wh  [#permalink]

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22 Feb 2019, 16:39
Bunuel wrote:
The average height of 40 students in a class is 172 cm. 30 students whose average height is 172.5 cm left the class and 40 students whose average height is 170.5 cm joined the class. Find the average height of the present class.

A. 170 cm
B. 170.2 cm
C. 170.5 cm
D. 175
E. 177 cm

The sum of the heights of the original 40 students is 40 x 172 = 6,880 cm.

The sum of the 30 students who left is 30 x 172.5 = 5,175 cm.

The sum of the 40 students who joined is 40 x 170.5 = 6,820 cm

So the new sum is 6,880 - 5,175 + 6,820 = 8,525 cm, and the new number of students is 40 - 30 + 40 = 50. Therefore, the new average height is 8,525/50 = 170.5 cm.

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Re: The average height of 40 students in a class is 172 cm. 30 students wh   [#permalink] 22 Feb 2019, 16:39
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