Tricks To Solve Questions On Average

Average is a basic chapter of arithmetic and is important to solve other Quantitative Aptitude problems. From the ‘average’ chapter many questions are regularly asked in different competitive exams.

Way to success:
Clear basic concepts, practice, concentration, Accuracy and speed are a must for ‘Average’ problems. Especially do concentration on calculation very carefully.

The Sum of all the numbers/elements/quantities divided by the total number of numbers/elements/quantities is called the Average.

Average =  (Sum of all numbers)/( Total number of numbers)

With the help of the Following Tricks, you can solve the problem of Average easily- 

Trick 1: The average of two or more numbers/quantities is called the mean of these numbers, which is given by 
Average(A) = (sum of observation/quantities)/(No.of observation/quantities)
∴S=A×n

Trick 2: The average of ‘n’ consecutive natural numbers starting from 1,2,3, ……n.
i.e. Average of 1,2,3, …..n =  (n+1)/2

Trick 3: The average of squares of ‘n’ consecutive natural numbers starting from 1 i.e.
Average of 1², 2², 3², 4² ….. x² = (n+1)(2n+1)/6

Trick  4: The average of cubes of first ‘n’ consecutive natural numbers 
i.e. Average of , 1³, 2³, 3³ ….. n3 =  n(n+1)²/4

Trick  5: The average of first ‘n’ consecutive even natural numbers 
i.e. Average of 2, 4, 6, ….. 2n = (n + 1)

Trick  6: The average of first ‘n’ consecutive odd natural numbers i.e. 1, 3, 5, ….. (2n – 1) = n

Trick  7: The average of certain consecutive numbers
a, b, c, ……… n is (a+n)/2

Trick 8: The average of 1st ‘n’ multiples of certain
numbers x = (x(1+n))/2

Trick  9: If A goes from P to Q with the speed of x km/h and returns from Q to P with the speed of y km/h, then the average speed of the total journey is
Average speed = 2xy/(x+y)

Trick 10: If a distance is travelled with three different speeds a km/h, b km/h and c km/h, then
The average speed of total journey =
=  3abc/(ab+bc+ca)  km/h

Practice Questions:

Q.1 A student calculates the arithmetic mean of the following 5 numbers: 10, 15, 20, 25 and x He found the mean is 15. Find out the value of x?

(1) 3 
(2) 7 
(3) 17 
(4) 5

Answer :-4
Solution:
Mean = (10+15+20+25+X)/5=15
70+X = 75
 X = 5

Q.2 The average of the marks obtained in a mock test by 8 boys was 50 and by 2 girls was 80. The average marks of all 10 students were –

(1)50 
(2) 56 
(3) 60 
(4) 62

Answer :-2
Solution:
Sum of total number of 8 boys in mock = 8 × 50 = 400
Sum of total number of 2 girls in exam = 2 × 80 = 160
Required average = (400+160)/10 = 560/10 = 56

Q.3 If the average weight of 5 girls is 20 kg; that of 3 girls is 15 kg, and that of the other 2 girls is 25 kg; then the average weight of all girls is-

(1) 15 kg 
(2) 11.5 kg 
(3) 16.5 kg 
(4) 19.5 kg

Answer:-4
Solution: 
Required Average 
= (20 X 5+ 15 X 3+ 25X2)/10 
= (100+45+50)/10 
= 195/10 
= 19.5 kg

Q.4 Total daily salary of the writers in geeks for geeks is 15000. The average daily salary of a writer is 750. Find the number of writers in geeks for geeks is –

(1) 16
(2)14 
(3) 20
(4)12

Answer:-3
Solution: 
Number of writers in geeks for geeks 

= 15000/750 = 20

Q.5 Out of 20 boys, 5 are each of 1 m 10 cm height, 10 are of 1 m 20 cm and rest of 1 m 30 cm. The average height of all of them is-

(1)1 m 10 cm
(2) 1 m 25 cm
(3) 1 m 20 cm
(4) 1 m 12 cm

Answer:-3
Solution:-

Average Height 
= (5 X 1.10 + 10 X 1.20 + 5 X 1.30)/20 
= (5.5 + 12 + 6.5)/20
= 24/20
= 1.20
= 1 meter 20 cm

Q.6 The average temperature for April, May, June and July month was 40°. The average temperature for May, June, July and December was 35°, If the temperature in April was 38°, then find the temperature in December (in degrees)

(1) 18° 
(2) 16° 
(3) 12° 
(4) 10°

Answer:-1
Solution:  
April + May + June + July = 4X40 = 160°       …. (i)
May + June + July + Dec = 4X35  = 140°        .. (ii)
From equation (I) & ( ii),we get
April – Dec = 160° – 140°
=> April – 20° = Dec
=> 38° – 20° =Dec
:. December = 18°

Q.7 In 2021, the average monthly income of an employee was 3,000. For the first nine months of the year, his average monthly income was 3100 and for the last four months, it was 4,500. His income in the ninth month of the year was –

(1) 16000 
(2) 5080  
(3) 8200 
(4) 9900

Answer:-4
Solution:  
Employee’s income in the eighth month 
= (3100 × 9 + 4 × 4500 – 12 × 3000) 
= (27900 + 18000 – 36000) 
= (45900 – 36000)
= 9900

Q.8 The average yearly expenditure of a company for the first five years is 25700, for the next two years 24900 and for the last five years 30300. If the company is saved 53200 during 12 years, the average yearly earnings of the company are (approx value, not exact value)-

(1) 30000 
(2) 31850 
(3) 31917 
(4) 35807

Answer:-3
Solution:  
Total expenditure of the company
= (5 × 25700 + 2 × 24900 + 5 × 30300)  
= (128500 + 49800 + 151500) 
= 329800
Total earning = (329800 + 53200) = 383000
Required average yearly earning = 383000/12 = 31917

Q.9 The average salary of all employees in geeks for geeks is Rs.24000. The average salary of 7 technicians is Rs.30000 and the average salary of the rest is Rs. 18000. The total number of workers in the workshop is- 

(1) 12 
(2) 16 
(3) 14 
(4) 15

Answer:-3
Solution:  
Let the Total number of employees in geeksforgeeks= P
Number of technicians = 7
Remaining employees = P – 7 
According to the question 
[(7 × 30000 + (P – 7 ) × 18000]/ P = 24000 
=> 7 × 30 + 18P – 126 = 24P 
=> 210 – 126 = 24P – 18P
=> 6P = 84
:. P = 14

Q.10 A man goes to the market from his house and returns house from the market at speeds of 10 km/hr and 15 km/hr respectively. Find out his average speed?

1) 12 km/hr
2) 15 km/hr
3) 14 km/hr
4) 13 km/hr

Answer:-1
Solution:-

We know,
Average speed = (2×S1×S2)/(S1+S2)
Here,S1 = 10 km/hr & S2 = 15 km/hr 
Average speed = 2×15×10/(15+10) km/hr 
                         = 300/25 km/hr
                         = 12 km/hr