Aptitude question and answer on Average

In this section we are going to discuss about average problems. Not just the overview of the topic, but also you are going to learn the important formulas on average along with explanation which is easy to understand.

33
The average of the first five multiples of 9 is:
A.    20
B.    27
C.    28
D.    30

Answer : B.   27

Explanation:
Required average = (total sum of multiple of 9)/5
= \((9+18+27+36+45)\over5\)
= 27

34
The average age of 50 students and a teacher is 25 years. When the teacher’s age is excluded, the average age decreases by 1 year. What is the age of the teacher?  
A.    65
B.    75
C.    74
D.    64

Answer : B.   75

Explanation:
Total age of 50 students and 1 teacher = \(25\times51 \)= 1275
Total age of the students = \(24\times50\) = 1200. ( Average age reduces by 1 when teachers age is not included )
Therefore the age of the teacher is 1275 – 1200 = 75 years.

35
Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average by 8 runs. His new average is:
A.    20
B.    21
C.    28
D.    32

Answer : C.  28

Explanation:
Let Ajit's average be x for 9 innings. So, Ajit scored 9x run in 9 innings.
In the 10th inning, he scored 100 runs then average became (x+8). And he scored \((x+8)\times10\) runs in 10 innings.
Now,
\(=>9x+100 = 10\times(x+8)\)
Or, \(9x+100 = 10x+80\)
Or, \(x = 100-80\)
Or, x = 20
New average = \((x+8) = 28\)  runs.