Averages Quiz Set 011

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Question 1

There are three sections in school with 30, 30 and 40 students respectively. The average weight of a student in these sections, respectively, is 6, 2 and 6 Kg. What is the average weight of all the the students of the combined sections?

 A

$4{4/5}$.

 B

$4{81/100}$.

 C

$4{79/100}$.

 D

$4{39/50}$.

Soln.
Ans: a

The sums of the weights of all the students is 30 × 6 + 30 × 2 + 40 × 6 = 480. The required average = 480/total students = $480/{30 + 30 + 40}$ = ${24/5}$, which is same as: $4{4/5}$.


Question 2

There is a sequence of 66 consecutive odd numbers. The average of first 26 of them is 82. What is the average of all the 66 numbers?

 A

122.

 B

123.

 C

121.

 D

120.

Soln.
Ans: a

The consecutive odd numbers form an AP with a common difference of 2. If the first term is a, then the average of first n terms of this AP is ${a + (a + (n-1) × 2)}/2$ which is = a + n-1. We are given the average of first 26 terms as 82. So a + 26 - 1 = 82, which gives a = 57. The average of first 66 terms would be a + 66 - 1 = 57 + 66 - 1 = 122.


Question 3

Average marks of class of 20 students is 85. What will be the average if each student is given 6 as grace marks?

 A

91.

 B

92.

 C

90.

 D

89.

Soln.
Ans: a

Let the total score of the class before grace marks be x. Then, by average formula $85 = x/20$, which gives x = $85 × 20 = 1700$. When grace marks = 6 are added for each of the 20 students, the new total becomes $1700 + 20 × 6 = 1820$, the new average becomes $1820/20 = 91$. TIP: As a shortcut, the new average = old average + grace marks.


Question 4

If the average of p and q is 20, the average of q and r is 54, and of r and p is 64, then what is the value of p?

 A

30.

 B

31.

 C

29.

 D

32.

Soln.
Ans: a

We have three equations (p + q)/2 = average of pq, (q + r)/2 = average of qr and (r + p)/2 = average of rp. Adding these three we get p + q + r = (average of pq + average of qr + average of rp) = (20 + 54 + 64) = 138. So p = 138 - (q + r) = 138 - (2 × average of q and r) = 138 - 2 × 54 = 30.


Question 5

The average weight of the 9 bogies of a train increases by 4 Kg when a new bogie replaces a bogie of weight 2 Kg. What is the weight of the new bogie.

 A

38.

 B

39.

 C

37.

 D

40.

Soln.
Ans: a

The total increase of weight = 9 × 4 = 36. So the weight of the new bogie = 2 + 36 = 38 Kg.


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This Blog Post/Article "Averages Quiz Set 011" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-10-26.

Posted by Parveen(Hoven),
Aptitude Trainer


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