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

Answer: Option B

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

Answer: Option B

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

Answer: Option C

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

Answer: Option C

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

Answer: Option B

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






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