Average

1. The average of first five even numbers are

A. 6

B. 9

C. 12

D. 15

Ans: A

Explanation:

$\text&space;{First&space;five&space;even&space;numbers&space;are&space;=&space;2,&space;4,&space;6,&space;8,&space;10}$

$\text&space;{Average}&space;=&space;\frac{2+4+6+8+10}{5}&space;=&space;\frac{30}{5}&space;=&space;6$

2. Three students got 60,72, and 66 marks in an exam respectively. Find the average.
A. 52

B. 58

C. 60

D. 66

Ans: D
Explanation:

$\text&space;{sum&space;of&space;observations}&space;=&space;60&space;+&space;72&space;+&space;66&space;=&space;198$

$\text&space;{Number&space;of&space;observations}&space;=&space;3$

$\text&space;{Average}&space;=&space;\frac{198}{3}&space;=&space;66$

3. The average cost of 5 mangoes is Rs.6. In them average of 3 mangoes is Rs.4.

find the average cost of remaining.

A. 5

B. 6

C. 9

D. 10

Ans: C

Explanation:

$\text&space;{Total&space;cost&space;of&space;5&space;mangoes}&space;=&space;5&space;\times&space;6&space;=&space;30$

$\text&space;{Total&space;cost&space;of&space;3&space;mangoes}&space;=&space;3&space;\times&space;4&space;=&space;12$

$\text&space;{Total&space;cost&space;of&space;2&space;mangoes}&space;=&space;30&space;-&space;12&space;=&space;18$

$\text&space;{Average&space;of&space;2&space;mangoes}&space;=&space;\frac{18}{2}&space;=&space;9$

4. Average age of 45 students is 12 years. Find the total age of the students.

A. 450

B. 540

C. 620

D. 680

Ans: B

Explanation:

$\text&space;{Average&space;age&space;of&space;students&space;=&space;12&space;years}$

$\text&space;{Number&space;of&space;students&space;=&space;45}$

$\text&space;{Total&space;age&space;of&space;students}&space;=&space;12&space;\times&space;45&space;=&space;540$

5. Find the average of first 20 multiples of 7.

A. 73.5

B. 70.5

C. 60.5

D. 75.5

Ans: A

Explanation:

$\text&space;{Required&space;average}&space;=&space;\frac{7\left&space;(&space;1+2+3+...+20&space;\right&space;)}{20}&space;=&space;\frac{1470}{20}&space;=&space;73.5$

6. The average of four consecutive even numbers is 27. Find the Largest of these numbers.

A. 26

B. 28

C. 30

D. 32

Ans: C

Explanation:

$\text&space;{Let&space;the&space;numbers&space;be&space;}x,&space;x+2,&space;x+\text{4&space;and&space;}x+6$

$\frac{x+&space;\left&space;(&space;x+2&space;\right&space;)+\left&space;(&space;x+4&space;\right&space;)&space;+&space;\left&space;(&space;x+6&space;\right&space;)}{4}&space;=&space;27$

$\frac{4x+12}{4}&space;=&space;27$

$x&space;+&space;3&space;=&space;27$

$x&space;=&space;24$

$\therefore&space;\text{The&space;largest&space;number}&space;=&space;\left&space;(&space;x+6&space;\right&space;)&space;=&space;24&space;+&space;6&space;=&space;30$

7. David obtained 76, 65, 82, 67 and 85 marks in English, Mathematics, Physics, chemistry and biology. His average was

A. 65

B. 69

C. 72

D. 75

Ans: D

Explanation:

$\text&space;{Average}&space;=&space;\left&space;(&space;\frac{76+65+82+67+85}{5}&space;\right&space;)&space;=&space;\left&space;(&space;\frac{375}{5}&space;\right&space;)&space;=&space;75$

8. Find the average of all the numbers between 6 and 34 which are divisible by 5.

A. 18

B. 20

C. 24

D. 30

Ans: B

Explanation:

$\text&space;{Average}&space;=&space;\left&space;(&space;\frac{10+15+20+25+30}{5}&space;\right&space;)&space;=&space;\left&space;(&space;\frac{100}{5}&space;\right&space;)&space;=&space;20$

9. A student was asked to find arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of  x ?

A. 3

B. 7

C. 17

D. 31

Ans: B

Explanation:

$\text&space;{clearly,}\left&space;(&space;\frac{3+11+7+9+15+13+8+19+17+21+14+x}{12}&space;\right&space;)&space;=&space;12$

$\left&space;(&space;\frac{137+x}{12}&space;\right&space;)&space;=&space;12$

$137&space;+&space;x&space;=&space;144$

$x&space;=&space;7$