# Problems on Averages: Set - 1

1. 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?
a) 8
b) 9
c) 10
d) 11
e) 12
2. In Arun's opinion, his weight is greater than 65 kg but leas 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 diferent probable weights of Arun?
a) 55.5 kg
b) 66.5 kg
c) 77.5 kg
d) 86.5 kg
e) 88.5kg
3. The average age of a husband and his wife was 23 years at the time of their marriage. After  five years they have a one-year old child. The average age of the family now is:
a) 18
b) 19
c) 20
d) 23
e) 25
4. A cicketer bas a certain average for 10 innings, In the eleventh inning, he scorod 108 runs, thereby increasing his average by 6 runs. His new average is :
a) 44 runs
b) 46 runs
c) 48 runs
d) 49 runs
e) 50 runs
5. The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
a) 3.6
b) 4.6
c) 6.5
d) 7.3
e) 7.5
6. The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
a) 70 kg
b) 75 kg
c) 80 kg
d) 85 kg
e) None of these
7. 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 ?
a) 35 years
b) 45 years
c) 51 years
d) 54 years
e) 55 years
8. The average age of a group of persons 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 age becomes 15.5 years. The number of persons initially going for picnic is :
a) 15
b) 20
c) 22
d) 23
e) 24
9. The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is :
a) 20
b) 30
c) 35
d) 40
e) 45
10. The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :
a) 20
b) 21
c) 22
d) 23
e) 24
Solution:
1. D) Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x = 22 or x = 11.
2. B) 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 = (66 + 67) / 2 = 66.5 kg
3. B) Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) + 1 = 57 years.
Required average = (57/3) = 19 years.
4. C) Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 6 => 11x + 66 = 10x + 108  =>  x = 42.
New average = (x + 6) = 48 runs.
5. B) Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6
6. D) Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
7. C) Age of the teacher = (37 * 15 - 36 * 14) years = 51 years.
8. B) Let the initial number of persons be x. Then,
16x + 20 * 15 = 15.5 (x + 20) <=> 0.5x = 10 <=> x = 20.
9. B) Total age increased = (8 * 2) years = 16 years.
Sum of ages of two new men = (21 + 23 + 16) years = 60 years
Average age of two new men = (60/2) years = 30 years.
10. B) Lot the total number of workers be v
Then,
8OOOv = (12000 * 7) + 6000 (v - 7) <=>  2000v = 42000  <=>  v = 21.