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Question 1 of 24
1. Question
The average attendance in a school for the first 4 days of the week is 30 and for the first 5 days of the week is 32. The attendance on the fifth day is
Hint
Attendance on the fifth day
= 32 × 5 – 30 × 4
= 160 – 120 = 40
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Question 2 of 24
2. Question
The average attendance of a class for the first three days of a month was 38. The average for the second, third and the fourth day was 42. The attendance on the fourth day being 42, find the attendance on the first day.
Hint
Total attendance for Day 1, 2, and 3
= 38 × 3 = 114
Total for Day 2, 3 and 4 = 126
Total for Day 2 and 3 = 126 – 42 = 84
Hence attendance on Day 1 = 114 – 84 = 30
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Question 3 of 24
3. Question
The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5, then the average of the whole group is :
Hint
and
∴
∴
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Question 4 of 24
4. Question
The average temperature for Monday, Tuesday and Wednesday was 55°, the average for Tuesday, Wednesday and Thursday was 60°, that for Thursday being 56°, what was the temperature on Monday?
Hint
Sum of temperature for Mon, Tue and Wed
= 55 × 3 = 165°
Sum of temperature for Tue, Wed and Thu
= 60 × 3 = 180°
Since temp. on Thursday = 56°
⇒ Temp for Tue and Wed = 180 – 56 = 124°
⇒ Temp of Monday = 165 – 124 = 41°
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Question 5 of 24
5. Question
Last year, a Home Appliance Store sold an average (arithmetic mean) of 42 microwave ovens per month. In the first 10 months of this year, the store has sold an average (arithmetic mean) of only 20 microwave ovens per month. What was the average number of microwave ovens sold per month during the entire 22 months period?
Hint
=
= 32 -
Question 6 of 24
6. Question
A car owner buys petrol at Rs 7.50, Rs 8.00 and Rs 8.50 per litre for three successive years. What approximately is his average cost per litre of petrol if he spends Rs 4000 each year?
Hint
Let average cost of petrol per litre be Rs x
Then
per litre -
Question 7 of 24
7. Question
The average age of 36 students in a group is 14 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?
Hint
Age of the teacher
= (37 × 15 – 36 × 14) years = 51 years.
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Question 8 of 24
8. Question
The average age of 24 students and the class teacher is 16 years. If the class teacher’s age is excluded, the average reduces by one year. What is the age of the class teacher?
Hint
Age of the CT
= 25 × 16 – 24 × 15 = 400 – 360 = 40 yrs.
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Question 9 of 24
9. Question
The average age of A and B is 20 years. If C were to replace A, the average would be 19 and if C were to replace B, the average would be 21. What are the age of A, B and C?
Hint
Given A + B = 40 …(i)
C + B = 38 … (ii)
A + C = 42 … (iii)
(i) + (ii) + (iii) ⇒ A + B + C = 60 …(iv)
From (i) and (iv), we get
C = 20 years
∴ B = 18 years and A = 22 years
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Question 10 of 24
10. Question
3 years ago the average age of a family of 5 members was 17 years. With the birth of a new baby, the average age of six members remains the same even today. Find the age of the new baby.
Hint
Sum of present ages of the six members
= (17 × 6) years = 102 years.
Sum of present ages of the 5 members (excluding baby)
= 5 × (17 + 3) years = 100 years.
∴ Age of the baby
= 102 – 100 = 2 years
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Question 11 of 24
11. Question
The average age of a group of person going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average becomes 15.5 years. Find the number of persons initially going for picnic.
Hint
Let the number of persons, initially going for Picnic = x
∴ Sum of their ages = 16x
Also,
⇒
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Question 12 of 24
12. Question
The average age of a board of 8 functional directors in a company is the same as it was 3 years ago, a younger man having been substituted for one of the directors. How much younger was the new man than the director whose place he took.
Hint
Let the new man was younger than the director = x years.
And 3 years ago, the sum of ages of board of directors = S – 8 × 3 = S – 24
Then, 3 years ago, average age of board of directors
Now,
⇒ x = 24 years
Shortcut Method : If the new young director would have been not substituted, then total age would have increased at present by 8 × 3 = 24 years.
Therefore, the new man is 24 years younger keeping the average at present same as 3 years ago.
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Question 13 of 24
13. Question
A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
Hint
Required average
=
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Question 14 of 24
14. Question
The captain of a cricket team of 11 players is 25 years old and the wicket-keeper is 3 years older. If the age of these two players are replaced by that of another two players, the average of the cricket team drops by 2 years. Find the average age of these two players.
Hint
Let average of team = x years
Then, 25 + 28 + S₉ = 11x … (i)
where S₉ is the sum of ages of remaining players
Also, Np + S₉ = 11(x – 2) , … (ii)
where Np is the sum of ages of new players
(i) – (ii) ⇒ 53 – Np = 22 ⇒ Np = 31
∴ Average age of new two players
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Question 15 of 24
15. Question
There are 50 boys in a class. Their average weight is 45 kg. When one boy leaves the class, the average reduces by 100 g. Find the weight of the boy who left the class.
Hint
Here one boy is excluded and final average of the group decreases.
∴ change in average is (-)ve = – 0.1 kg.
Using the formula
Sum of the quantities excluded
⇒ weight of the boy who left
= (1 × 45) – (– 0.1 × 49) = 49.9 kg
∴ Weight of the boy who left the class is 49.9 kg.
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Question 16 of 24
16. Question
The average weight of 45 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
Hint
Total weight of 45 students
= 45 × 52 = 2340 kg
Total weight of 5 students who leave
= 5 × 48 = 240 kg
Total weight of 5 students who join
= 5 × 54 = 270 kg
Therefore, new total weight of 45 students
= 2340 – 240 + 270 = 2370
⇒ New average weight
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Question 17 of 24
17. Question
In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun’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 of them are correct in their estimation, what is the average of different probable weights of Arun?
Hint
Let Arun’s weight be X kg.
According to Arun,
65 < X < 72.
According to Arun’s brother,
60 < X < 70.
According to Arun’s mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
∴ Required average
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Question 18 of 24
18. Question
The average marks scored by Ganesh in English, Science, Mathematics and History is less than 15 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
Hint
⇒ G – S = 60
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Question 19 of 24
19. Question
A pupil’s marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is:
Hint
Let there be x pupils in the class.
Total increase in marks
=
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Question 20 of 24
20. Question
In an examination, a pupil’s average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?
Hint
Let the number of papers be x. Then,
63x + 20 + 2 = 65x
⇒ 2x = 22
⇒ x = 11.
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Question 21 of 24
21. Question
The average of marks obtained by 120 candidates was 35. If the average of the passed candidates was 39 and that of the failed candidates was 15, then the number of those candidates who passed the examination, was
Hint
∴ Required ratio = 20 : 4 = 5 : 1
∴ Number of passed candidates
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Question 22 of 24
22. Question
A school has 4 section of Chemistry in Class X having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student
Hint
Required average marks
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Question 23 of 24
23. Question
A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 36 instead of 86 then find the correct average marks upto two decimal places.
Hint
Correct average
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Question 24 of 24
24. Question
The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. Find his highest score.
Hint
Total runs = 40 × 50 = 2000
Let his highest score be =x
Then his lowest score = x – 172
Now
⇒ 2x = 2172 – 1824
⇒ x = 174
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