Aptitude : Problems on Average

(11) The average age of a husband and wife is 23 years when they were married 5 years ago. The average age of the husband, wife and their child who was born during the interval, is 20 years now. How old is the child now?

• (a)4 years
• (b)3 years
• (c)2 years
• (d)5 years

Answer

Correct Answer : (a) 4 years
The total age of the husband and wife 5 years ago is 23 x 2 = 46 years.
The total age of the husband and wife now is 46 + 5 x 2 = 56 years.
The total age of the husband, wife and child now is 20 x 3 = 60 years.
Therefore, the age of the child now is 60 – 56 = 4 years.

(12) The average of 5 consecutive numbers is n. What is the value of the smallest number?

• (a)n
• (b)n – 2
• (c)n+2
• (d)0

Answer

Correct Answer : (b) n – 2
The value of the smallest number is n – 2.
Let the five consecutive numbers be x, x + 1, x + 2, x + 3, and x + 4.
The average of these numbers is n.
This means that (x + (x + 1) + (x + 2) + (x + 3) + (x + 4)) / 5 = n
This simplifies to 5x + 10 = 5n
This further simplifies to x + 2 = n
Therefore, the value of the smallest number is n – 2.

(13) The average of three numbers is 20. If two of the numbers are 15 and 16, what is the third number?

• (a)27
• (b)28
• (c)29
• (d)30

Answer

Correct Answer : (c) 29
The average of three numbers is the sum of the numbers divided by 3. Since the average is given as 20, the sum of the three numbers is 20 * 3 = 60.
If two of the numbers are 15 and 16, their combined sum is 15 + 16 = 31.
To find the third number, subtract the combined sum of the first two numbers from the total sum of all three numbers. So, the third number is 60 – 31 = 29.

(14) The average age of a group of 10 friends is 15. If one friend leaves, the average age becomes 16. How old is the friend who left?

• (a)6 years old
• (b)7 years old
• (c)8 years old
• (d)9 years old

Answer

Correct Answer : (a) 6 years old
The total age of the group of 10 friends is the average age multiplied by the number of friends, or 15 * 10 = 150 years.
When one friend leaves, there are 9 friends left, and the average age is 16 years. So, the combined age of the remaining friends is 16 * 9 = 144 years.
The age of the friend who left is the total age of the group of 10 friends minus the combined age of the 9 remaining friends, or 150 – 144 = 6 years.
So, the friend who left is 6 years old.

(15) The average weight of a group of people is 75 kg. If one person weighing 60 kg leaves the group, the average weight of the group becomes 78 kg. How many people were in the group initially?

• (a)5.5 people in the group.
• (b)4.5 people in the group.
• (c)6 people in the group.
• (d)7 people in the group.

Answer

Correct Answer : (c) 6 people in the group.
Let’s denote the total number of people initially in the group as N and their total weight as W. We know that:
The initial average weight is 75 kg, so W = 75N.
If a 60 kg person leaves, the total weight becomes W – 60, and the number of people becomes N – 1.
The problem states that the new average weight after the person leaves is 78 kg. Therefore, we have:
(W – 60) / (N – 1) = 78
Substitute W from the first equation into the second:
(75N – 60) / (N – 1) = 78
75N – 60 = 78N – 78
78 – 60 = 78N – 75N
18 = 3N
N = 18 / 3 = 6
So, there were initially 6 people in the group.