**Averages | Mathematical Reasoning | Important For UGC NET Paper 1**

** ****Averages :-** The average is the mean value, which is the ratio of the sum of the values in a given set to all the values in the set.

**Average = Total Sum of observations / Total Number of observations**

1 In the first 10 overs of a cricket game, the run rate was only 5.2, What should be the run rate in the remaining 10 overs to reach the target of 182 runs

solution :-

Total over in game = 20

Firstly completed over = 10

Run rate = 5.2 (i.e. average)

Hence total run = 10 * 5.2 = 52

Target run = 182

Required run = 182 – 52 = 130

Remaining over = 10

So, Required run rate = 130 / 10

Required run rate = 13

2. Two parents, two grandparents, and three grandkids make up a family. The grandparents are 67 years old, the parents are 35 years old, and the grandchildren are 6 years old on average. What is the family’s average age

solution :-

Total member in a family =

2 parents + 2 grandparents + 3 grandkids = 7

Ages of parents. = 2 * 35 = 70 yrs

Ages of grandparents = 2 * 67 = 134 yrs

Ages of grandchildren = 3 * 06 = 18 yrs

Overall ages of family members = 70 + 134 + 18

So, the family’s age = 222

So, the family’s average age = 222 / 7 = 31.7

3 A business has a sale of Rs. 6485, Rs. 6787, Rs. 6455, Rs. 7290 and Rs. 6762 for 5 consecutive Days. How much sale must he have in the sixth Days so that he gets an average sale of Rs. 6600

solution :-

Let, sale of six days = x

And average sale of all six days = 6600

So, overall sale of six days = 6600 * 6 = 39600

Now ,

Steps 1 :- 6485 + 6787 + 6455 + 7290 + 6762 + x = 6600 * 6

Steps 2 :- 33779 + x = 39600

Steps 3 :- x = 39600 – 33779

The sixth Days sales required is = 5821

4 If the three batches of 55, 60, and 45 students have average marks of 50, 55, and 60, respectively, then the overall average score is:

solution :-

Here, total marks of first batch = 55 * 50 = 2750

Total marks of second batch = 60 * 55 = 3300

Total marks of third batch = 45 * 60 = 2700

Hence overall marks of all three batches = 8750

And total number of students in all three batches = 160

Then average marks = 8750 / 160 = 54.68

5 The average weight of 10 person’s increases by 2 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of new person

solution :-

In this question, one condition apply

If average of all number increase by any value ‘a’ then every number increase by that value ‘a’

Here, average value increase by 2 kg.

So, weight of all 10 persons increased by 2 kg. i.e. 10 * 2 = 20 kg.

So, after replacement of 65 kg person

Weight of new person is, 65 + (10 * 2) = 65 + 20 = 85 kg.

**Important Averages Question for UGC NET Exam preparation and Put the answer on comment.**

1 P and Q make an average monthly salary of Rs. 5050. Q and R make an average monthly income of Rs. 6250, while P and R make an average monthly income of Rs. 5200. P’s monthly take-home pay is

2 Three years ago, the average age of the couple with a child was 27 years old, and five years ago, it was 20 years old. The husband’s age at this time is

3 For three years in a row, a car owner purchases petrol for Rs. 75.50, Rs. 80 and Rs. 85.50 a litre. If he spends Rs. 40000 annually, what is the typical price per litre of petrol

4 Arun estimates that he weighs more than 65 kg but less than 72 kg. In contrast to Arun, his brother believes that Arun weighs more than 60 kg but less than 70 kg. According to his mother, he shouldn’t weigh more than 68 kg. What is the average of the several estimated weights of Arun, assuming that everyone was accurate in their estimation

5 A, B, and C all weigh about 45 kg on average. The weight of B is 40 kg if the average weights of A and B are 43 kg and B and C are

6 In a class of 16 guys, the average weight is 50.25 kg, while the weight of the remaining 8 boys is 45.15 kg. Find out the class’s male students’ average weights.

7 An average library has 510 visits on Sundays and 240 visitors on other days. In a month of 30 days starting on a Sunday, the average daily visitors are

8 The incorrect entry for a student’s grade was 83 instead of 63. As a result, the average grade for the class was raised by half. The number of students in the class.