# Examples(Set 2) - Average

6.A student's mark was wrongly entered as
83
instead of
63.
Due to that the average mark of the class got increased by
1/
2
. What is the number of students in the class?

A.
45

B.
40

C.
35

D.
30

Explanation:

Let total number of students be x

Increase in average mark = 1/ 2

Increase in total mark = x( 1/ 2)

= x/ 2

But increase in total mark = 83 − 63

= 20

Therefore, x/ 2 = 20

⇒ x = 40

7.A library has an average of
510
visitors on Sundays and
240
on other days. What is the average number of visitors per day in a month of
30
days beginning with a Sunday?

A.
304

B.
285

C.
270

D.
290

Explanation:

In a month of 30 days beginning with Sunday, there are 4 complete weeks and another two days, Sunday and Monday.

Hence there are 5 Sundays and 25 other days.

Average visitors on Sundays = 510

Total visitors of 5 Sundays = 510 × 5

Average visitors on other days = 240

Total visitors of other 25 days = 240 × 25

Total visitors = 510 × 5 + 240 × 25

Total days = 30

Average number of visitors per day = (510 × 5 + 240 × 25)/ 30

= 285

8. The average weight of
16
boys in a class is
50.25
kg and that of the remaining
8
boys is
45.15
kg. Find the average weights of all the boys in the class.

A.
42.25
kg

B.
51.25
kg

C.
48.55
kg

D.
50
kg

Explanation:

Average weight of 16 boys = 50.25

Total weight of 16 boys = 50.25 × 16

Average weight of remaining 8 boys = 45.15

Total weight of remaining 8 boys = 45.15 × 8

Total weight of all boys in the class = 50.25 × 16 + 45.15 × 8

Total number of boys = 16 + 8 = 24

Average weight of all the boys = (50.25 × 16 + 45.15 × 8)/ 24

= 48.55

9.In Rugved's opinion, his weight is greater than
65
kg but less than
72
kg. His brother does not agree with Rugved and he thinks that Rugved's weight is greater than
60
kg but less than
70
kg. His mother's view is that his weight cannot be greater than
68
kg. If all are them are correct in their estimation, what is the average of different probable weights of Rugved?
A.
61
kg B.
70
kg
C.
67
kg D.
69
kg

Explanation:

Let Rugved's weight be x

According to Rugved, 65 smaller than x greater than 72

According to brother, 60 smaller than x greater than 70

According to mother, x smaller than equal to 68

Given that all the above conditions are true. Therefore we have 65 smaller than x greater than equal to 68

That is, x can be 66 , 67 , or 68

Average of different probable weights of Rugved = average of 66 , 67 , 68

(66 + 67 + 68)/ 3

= 67.

10. A car owner buys diesel at
₹
7.50
,
₹
8
and
₹
8.50
per litre for three successive years. What approximately is the average cost per litre of diesel if he spends
₹
4000
each year?

A.
₹
8.1

B.
₹
7.98

C.
₹
7.4

D.
₹
8

Explanation:

Total quantity of petrol consumed in 3 years =( 4000/7.50 + 4000/8 + 4000/8.50 )litres

=( 76700 /51)litres

Total amount spent =Rs.(3×4000)=Rs.12000.

∴ Average cost =Rs. (12000×51)/76700

=Rs.7.98