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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?

### 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.

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 2020-02-07. Published on: 2016-04-22