Average is defined as the ratio of sum of all observations in a group to the number of observations in the group.
$$Average = \left( {{Sum \ of \ observations} \over {Number \ of \ observations}} \right)$$
A man covers a certain distance at ‘a’ km/h and return ‘b’ km/h. Then the average speed during the whole journey is: $${2ab}\over{a+b}$$
1The average age of Banerjee's
family consisting of 4 members, 4 years ago, was 28 years. 2 years ago, a baby was born in the family. The average age of the family 2 years from now would be :
A
25 years
B
22 years
C
28 years
D
30 years
Correct Ans:C
Explanation:
4 years ago, total age of 4 members = 4×28 = 112 years
Present age of 4 members = 112+(4×4) = 128 years
New born baby present age = 2 years
So, present age of 5 members = 128 + 2 = 130 years
2 years hence the total age of the family = 130 + (5×2) = 140 years
Average age of the family two years hence = 140 / 5 = 28 years
C
2The average age of a class of 39 students is 15 yr. If the age of the teacher is included, then the average increases by 3 months. Find the age of the teacher:
A
25
B
28
C
16
D
31
Correct Ans:A
Explanation:
Average age of 39 students = 15 yr Age of 39 students = 39 × 15 = 585 yr Average age of students and teacher = 15 + 3 months = 15 + 3/12 = 61/4 yr Age of students and teacher = 40 × 61/4 = 610 yr Hence, age of teacher = 610 - 585 = 25 yr
A
3 The average of 19 numbers is 8. If the average of the first 9 numbers be 11 and the average of last 9 numbers be 9, then the middle number is?
A
21
B
40
C
28
D
30
Correct Ans:B
Explanation:
As per the given information, we get Average of 19 numbers = 8. So, total of the numbers = 19× 8 = 152 Average of first 9 numbers = 11. So, total of the numbers = 11 × 9 = 99 Average of last 9 numbers = 9. So, total of the numbers = 9 × 9 = 81 Hence, the 10th number = (99+81) - 152 = 180- 152 = 28. Hence, the answer is 28.
B
4 Biky
got married 5 years ago, today her age is $$1\frac{1}{3}$$ time her age at the time of marriage. What is present age of Biky
(in years)?
A
30
B
24
C
15
D
20
Correct Ans:D
Explanation:
Let present age be x Let the age of Biky
when she got married =×- 5 x = (x - 5) × (4/3) 3x = 4x - 20 4x - 3x = 20 x = 20 The present age of Biky
is 20 years.
D
5The average age of Lusi and Rani
is 18 years. When Rita replaces Rani
, the average age is increased by 1 and when Rani
replaces Lusi the average age becomes 17 years. What is the age of Rita?
A
15 years
B
16 years
C
17 years
D
18 years
Correct Ans:18 years
Explanation:
Given, average age of Lusi and Rani
= 18 years
⇒ Total age of Lusi and Rani
= Average × 2
= 18 × 2 = 36
⇒ Lusi + Rani
= 36 ⇒ eqn(1)
When Rita replaces Rani
,
Average age of Lusi and Rita = 19 years
⇒ Total age of Lusi and Rita = 19 × 2 = 38
⇒ Lusi + Rita = 38 ⇒ eqn(2)
When Rani
replaces Lusi,
Average age of Rani
and Rita = 17 years
⇒ Total age of Rani
and Rita = 17 × 2 = 34
⇒ Rani
+ Rita = 34 ⇒ eqn(3)
Now, Subtracting eqns (1) and (2) i.e., eqn (2) - eqn (1), we get,
Rita - Rani
= 38 - 36
⇒ Rita - Rani
= 2 ⇒ eqn (4)
Now, eqn(3) + eqn (4), we get
2 Rita = 34 + 2
⇒ Rita = 36/2
⇒ Rita = 18
Thus, the age of Rita = 18 years.
D
6The average of 8 numbers is 14. The average of 6 of these numbers is 16. What is the average of the remaining two numbers?
A
9
B
8
C
10
D
11
Correct Ans:B
Explanation:
Average of 8 numbers = 14 Sum of 8 numbers = 14×8 = 112 Similarly, average of 6 numbers = 16 Sum of 6 numbers = 16×6 = 96 ∴ Sum of remaining two numbers = Sum of 8 numbers - Sum of 6 numbers = 112 - 96 = 16 Average = Sum of two number/2 =16/2 Average =8
B
7The average weight of 17 boxes is 92 kg. If 18 new boxes are added, the new average increases by 3 kg. What will be the average weight of the 18 new boxes?
A
99.2 kg
B
95.2 kg
C
97.8 kg
D
93.8 kg
Correct Ans:C
Explanation:
average weight of 17 boxes = 92 kg
So, weight of 17 boxes = 17×92 = 1564 kg
If 18 boxes are added, the average weight increases by 3 kg
∴ total number of boxes= 17 + 18 boxes = 35 boxes
Total weight of 35 boxes = 35×(92 + 3) = 3325 kg
∴ weight of 18 boxes = 3325 - 1564 = 1761 kg
Thus, average weight of 18 boxes = 1761/18 = 97.8 kg:
C
8Find the average of all the odd numbers and average of all the even numbers from 1 to 45:
A
21
B
22
C
23
D
24
Correct Ans:C
Explanation:
Details
C
9 The average age of 33 students and the class teacher in a class is 15 years. If the class teacher's age is 48 years. What would be the average age of only the students?
A
14 years
B
18 years
C
13 years
D
17 years
Correct Ans:A
Explanation:
Given: Average age of 33 students and a teacher = 15 yrs Age of teacher = 48 yrs Total age of all students = (15×34) - 48 = 510 - 48 = 462 yearss Required average age = 46$$\frac{2}{3}$$3 =14 yrs ∴ average age of students = 14yrs.
A
10The average age of a group of 10 students was 14. The average age increased by 1 years when two new students joined the group. What is the average age of the two new students who joined the group?
A
27
B
25
C
23
D
20
Correct Ans:D
Explanation:
The average age of a group of 10 students is 14.
∴ the sum of the ages of all 10 of them = 10 × 14 = 140
When two students joins the group, the average increase by 1. New Average = 15
Now there are 12 students ∴ sum of all the ages of 12 students = 15×12 = 180
∴ the sum of the ages of two students who joined = 180 - 140 = 40
And the average age of these two students = 20
