# Averages Questions with Answers

## Questions and Answers for Averages

In this Page you will Find Averages Questions with Answers that will help in Different Examinations. The questions are prepared based on the concept of averages  and as per the latest exam pattern.

## Averages Formulas

### Concept of Averages :

The concept of averages refers to a way of summarizing a set of numbers by finding a representative value that is in some sense in the middle of the data. Averages are useful for understanding and analyzing data, and they come in several forms, each with its own specific purpose.

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1. The run rate in cricket given for the first 10 overs was 3.2. Calculate the run rate in rest of the 40 overs in order to score 282 runs.

3.5

3.5

7.95%

4.0

4.0

8.47%

6.25

6.25

75.7%

Cannot be determined

Cannot be determined

7.88%

Run rate = $\frac{(282−3.2 \times 10)}{40}$

= $\frac{250}{40}$

= 6.25

2. In a family, two grandparents, three grandchildren, and two parents. 67 years is the average age of the grandparents. 35 years is the average age of the parents. 6 years is the average age of the children. Calculate the average age of the family.

25

25

5.91%

40

40

9.88%

31.71

31.71

77.03%

Cannot be determined

Cannot be determined

7.18%

Family average age = $\frac{(67\times 2+35\times 2+6\times 3)}{2+2+3}$

= $\frac{(134+70+18)}{7}$

= $\frac{222}{7}$

= 31.71

3. A shopkeeper has a sale of Rs. 6359, Rs. 2365, Rs. 5698, Rs. 5690, and Rs. 4560 for 5 successive months. Calculate his sale in the sixth month to make an average sale of Rs. 6400.

12348

12348

11.11%

13728

13728

73.59%

23614

23614

10.33%

Cannot be determined

Cannot be determined

4.97%

Sale for 5 months= 6359 + 2365 + 5698 + 5690 + 4560 = 24672

Required sale = (6400 x 6) - 24672

= 38400- 24672

= 13728

4. If zero is the average of 20 numbersthen how many of them, at most must be greater than zero?

19

19

49.88%

5

5

6.95%

10

10

16.79%

Cannot be determined

Cannot be determined

26.39%

Average = 0

Therefore, the sum of 20 numbers= 0 x 20 =0

19 numbers among them may be positive.

If the sum of these numbers is a, then the 20th number is –a.

5. When a new man joins a group of 8 people, their average age increases by 2.5kg. If he replaces a man weighing is 55 kg, how much does he weigh?

80

80

7.67%

75

75

73.91%

65

65

12.03%

Cannot be determined

Cannot be determined

6.39%

Increased weight = (8 x 2.5) =20

Weight of the new man = (55 +20) = 75

6. 11 players make a football team. The captain’s age is 25 years. Age of the goalkeeper is 4 years more than that of the captain. The average age of the remaining team members except from these two is one year more than the entire team’s average age. What is the average age of the team?

31.5

31.5

65.4%

32

32

12.53%

26

26

17.23%

Cannot be determined

Cannot be determined

4.83%

Average age of team = x

Therefore, 11x – (25 +29) = 9 (x+1)

11x – (25 +29) = 9 (x+1)

11x – 54 = 9x + 9

11x – 9x = 9 + 54

2x= 63

x = $\frac{63}{2}$

=31.5

7. The average monthly income of A and B is Rs. 5050, that of B and C is Rs. 6250, and that of A and C is Rs. 5200. Calculate the monthly income of A.

3000

3000

10.91%

5000

5000

15.47%

4000

4000

70.58%

Cannot be determined

Cannot be determined

3.04%

A + B = 5050 x2 = 10100 -----(i)

B + C = 6250 x 2 = 12500-----(ii)

C + A = 5200 x 2 = 10400-----(iii)

Adding the above three equations, we get,

2 (A + B + C) = 33000

Or, A + B + C = 16500-----(iv)

When we subtract (ii) from (iv), we get

A = 4000

Therefore, A’s monthly income = Rs. 4000

8. The average age of Alice, Bob, and Mike three years ago was 35 years.  5 years back the average age of Bob and Mike is 20 years. Determine Alice’s present age.

64

64

71.23%

20

20

11.28%

35

35

13.68%

Cannot be determined

Cannot be determined

3.81%

Sum of present ages = (35 x 3 + 3 x 3) years = 114

present age of Bob and Mike = (20 x 2 + 5 x 2) years = 50

Therefore, Alice’s age = 114 – 50

= 64

9. Ravi buys a petrol at Rs. 7.50, Rs. 8, and Rs. 8.50 for 3 months. Calculate the approximately average cost per liter of petrol if he spends Rs. 4000 each month.

8.0

8.0

31.97%

7.98

7.98

59.54%

10

10

6.36%

Cannot be determined

Cannot be determined

2.12%

Total fuel consumed in 3 months = $(\frac{4000}{7.50}+\frac{4000}{8}+\frac{4000}{8.50})$

= $4000 (\frac{2}{15}+\frac{1}{8}+\frac{2}{17})$

= $\frac{76700}{51}$ litres

Total money spent = 3 x 4000 = 12000.

Therefore, average cost = $12000 \times \frac{51}{76700}$

= $\frac{6120}{767}$

= 7.98

10. Ajay thinks that his weight is somewhere in between 65 and 72 kg. Ajay’s sister disagrees and says that his weight is more than 60 kg but less than 70 kg. His father thinks that his weight must not be more than 68 kg. If all of them are correct, what is the average possible weight of Ajay?

59

59

8.49%

80

80

7%

67

67

80.92%

Cannot be determined

Cannot be determined

3.58%

Let Ajay’s weight = x kg

Age assumed by Ajay, 65 < X < 72

Age assumed by sister, 60 < X < 70.

Age assumed by father, X <= 68

Favourable values = 66, 67 and 68.

Average = $\frac{(66+67+68)}{3} = \frac{201}{3} = 67$ kg

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