QUESTIONS ON AVERAGE (PART-3)

QUERY 21

The average of marks scored by 35 students is 72. If the marks secured by 1 student were written as 36 instead of 86, find the current average.

A) 73
B) 73.43
C) 75
D) 74.25

MAHA GUPTA
Total of marks to be increased due to error = 86 – 36 = 50

But this error will effect the average of all 35 students
Therefore, average to be increased = 50/35 = 1.43 (appox)

Hence the current average = 72 + 1.43 = 73.43 (option ‘B’)

QUERY 22

Average of marks scored by some students in an exam was found to be 60. After the error having been corrected, the average of 100 students became 30 and for all the students the average came down to 45. Find the number of students appeared in that exam.

A) 150
B) 175
C) 200
D) 250

MAHA GUPTA
Let the total number of students appeared = x
Thus, incorrect total of marks = 60x
And correct total of marks = 45x

Total marks of 100 students according to the incorrect average = 100*60 = 6,000
Their correct total = 100*30 = 3,000
Total of 100 students that was wrongly included = 6,000 – 3,000 = 3,000

Now wrong total of marks = correct total of marks + wrongly included marks
60x = 45x + 3,000
=> x = 200

Therefore the total students appeared = 200 (option ‘C’)

NOTE: This question can speedily be done by answer options.

QUERY 23

The average age of family of 10 members is 20 years. If the age of the youngest member of the family is 10 years, then the average age of the members of the family just before the birth of the youngest member was approximately?

A) 11.1
B) 12.5
C) 14.25
D) 14.01

MAHA GUPTA
Total present age of the family = 10*20 = 200 years

Total age of the family 10 years ago (just before the year of the birth of the youngest members) = 200 – 10*10 = 100 years

Numbers of the members before the birth = 9

Therefore average age at that time = 100/9 years = 11.1 (options ‘A’)

QUERY 24

Out of 10 teachers of a school one teacher retires and in his place a new teacher of age 25 years joins. As a result the average age of teachers is reduced by 3 years. The age in years of the retired teacher is?

A) 60 years
B) 62 years
C) 58 years
D) 55 years

MAHA GUPTA
Age of the retired teacher = Age of the new teacher + Total decrease in age = 25 + (10*3) = 55 years (option ‘D’)

QUERY 25

Average age of five men is 26; one 35-year old man joins them. What is the new average?

A) 27.5
B) 27.75
C) 31.25
D) 31.83

MAHA GUPTA
Age increased due to joining of new man = His actual age – Average age = 35 – 26 = 9

But the number of men now is 6
So, the average age increased = 9/6 = 1.5

Therefore the new average = 26 + 1.5 = 27.5 (option ‘A’)

QUERY 26

When the average age of husband, wife and their son was 42 years, the son got married and a child was born just one year after the marriage. When child turned to be 5 years then the average age of the family became 36 years. What was the age of the daughter-in-law at the time of marriage?

A) 26 years
B) 25 years
C) 24 years
D) 23 years

MAHA GUPTA
Total age of husband, wife and their son at the time of marriage of their son = 42*3 = 126 years
When the child is 5 years old, 6 years passed as it was born after 1 year of marriage
So increase in their age = 6*3 = 18 years
Increase in the age of daughter-in-law after marriage = 6 years
Child’s age now = 5 years

Total age of all 5 members now = 36*5 = 180 years
Therefore daughter’s-in-law age at the time of marriage = 180 – (126+18+6+5) = 180 – 155 = 25 years (option ‘B’)

QUERY 27

In a school, the average age of students is 6 years, and the average age of 12 teachers is 40 years. If the average age of the combined group of all the students and teachers is 7 years, then the number of students is?

A) 396
B) 400
C) 408
D) 416

MAHA GUPTA
Let the number of students be x
Then, 6x +12*40 = (x + 12)*7
=> x = 396 (option ‘A’)

ANOTHER METHOD
We can also do this sum by applying Allegation Method, see how

STUDENTS                     TEACHERS

We see, STUDENTS : TEACHERS = 33 : 1
Teachers = 1 ratio = 1*12 = 12
Therefore, number of students = 33*12 = 396 (option ‘A’)

TRICK
Check with given answer options, you can do this in seconds. For example take 396
396*6 + 12*40 ÷ 396+12
= 7, which is correct