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 Average Questions**

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

**Average Questions With Answers**

**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 :**

**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 :**

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: **

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: **

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

**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 : **

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 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

#### D. Data inadequate

**Solution: **

Weight of new person = (65 + 20) kg = 85 kg.