Averages

08 May 2020

Average is mainly defined as the sum of observations divided by the number of observations. As in Quantitative aptitude test questions asked on Averages can be solved if the concept is enough clearly understood. Lets recall  the concept, understand it and apply them to solve varirty of problems.

Formula's For Averages

Average = Sum Of Observations / No Of Observations

Group 1

Average = A1
Sum of Obs = S1
Number of Obs. = N1

Group 2

Average = A2
Sum of Obs = S2
Number of Obs. = N2

If Group 1 and Group 2 come together then the combined average of the group will be A = S1 + S2 / N1 + N2

Problem of Replacement (Most Common Type of Problem in Averages) :

If Average of a group of N people increases/decreases by P kg when one or more persons weighing W kg is replaced by a new person. Then, the weight of new person is:  W+ P x N (if average increases)   W- P x N (if
average decreases)

Eg.

The average weight of 5 persons is decreased by 2kg when one of the men whose weight is 50kg is replaced by a new man. The weight of the new man is

In this problem average decrease hence weight of new person is: 50 – 5x2= 40 kg

Practice Questions For Averages

Q1) There are two sections A and B of a class, consisting of 36 and 44 students’ respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class.

A) 30.00 kg

B) 35.00 kg

C) 37.25 kg

D) 42.50 kg

Solution :

Q2) The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 33 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. Find out the average age of the team.

A) 21 years

B) 23 years

C) 24 years

D) 20 years

Solution :

Q3) The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, then find the average for the last four matches.

A) 33.25

B) 33.5

C) 34.25

D) 35

Solution :

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Q4) The distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km per hour. Find the average speed of train during the whole journey.

A) 60.3 km/hr

B) 35.0 km/hr

C) 57.5 km/hr

D) 57.5 km/hr

Solution :

Q5)In the first 10 overs of a cricket game, the run rate was only 3.2.  What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

A. 6.25

B. 5.5

C. 7.4

D. 5

Solution :

Runs scored in the first 10 overs = 10 × 3.2 = 32
Total runs = 282
Remaining runs to be scored = 282 - 32 = 250
Remaining overs = 40
Run rate needed = 250/40=6.25

Q6) The mean weight of a group of seven boys is 56 kg. The individual weights (in kg) of six of them are 52, 57, 55, 60, 59 and 55. Find the weight of the seventh boy.

A. 64

B. 54

C. 88

D. 28

Solution:

Mean weight of 7 boys = 56 kg.
Total weight of 7 boys = (56 × 7) kg = 392 kg.
Total weight of 6 boys = (52 + 57 + 55 + 60 + 59 + 55) kg= 338 kg.
Weight of the 7th boy = (total weight of 7 boys) - (total weight of 6
boys)
= (392 - 338) kg = 54 kg.
Hence, the weight of the seventh boy is 54 kg.

Q7)  Average of 16 numbers is 8. If 2 is added to every number, the  new average will be:

A) 13

B) 9

C) 10

D) 8

Solution:

Average of 16 numbers = 8
Thus, total of 16 numbers = 16 * 8 = 128
When 2 is added to every number then total of 16 numbers increases
by 16 * 2
= 32
Thus, new total of 16 numbers = 128 + 32 = 160
New average of 16 numbers = 160 / 16 = 10

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Q8) The average weight of 15 girls in a group is 24 kg when a new girl included  the average weight increases by 2. What is the weight of the new girl?

A. 56 kg

B. 28 kg

C. 34 kg

D. none of these

Solution :

Average weight of 15 girls = 24 kg
Total weight of 15 girls = 24 x 15 = 360 kg
Average after including a new girl = 24 + 2 = 26 kg
Total weight of 16 girls = 26 x 16 = 416 kg
Weight of the new girl = Total weight of 16 girls - Total weight of 15
girls = 416 - 360 = 56 kg. Hence the required answer is 56 kg.

Q9) Average weight of 25 boys in a class is 48 kgs. The average weight of the class of 40 students is 45 kgs. What is the average weight of the 15 girls in the class?

A. 44 kgs

B. 42 kgs

C. 40 kgs

D. 39 kgs

Solution:

Total weight of boys in the class = 25 *48 = 1200 kgs
Total weight of all students in the class = 45 * 40 = 1800 kgs
Total weight of the girls in the class = 1800 - 1200 = 600 kgs
Average weight of girls = 600/15 = 40 kgs

Q10) The average weight of 8 person's increases by 2.5 kg when a new  person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

A. 76 kg

B. 76.5 kg

C. 85 kg

Solution:

Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.

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