Quantitative Aptitude

Averages

1,527 Questions
All Basic average and reverse calculation 405 Adding or removing an observation 342 Weighted and combined averages 320 Replacement and correction of a recorded value 233 Ratio shortcut for two-group mixtures 111 Equal-distance average speed 59 Age, score, weight, and spending applications 32 Consecutive terms and arithmetic progressions 25

Averages Questions

Multiple choice softskills business skills

What is the average weight of the class-if the average weight of boys in the class is 50 and average weight of girls in the class is 40. The ratio of number of boys to girls in 2:3

  1. 55

  2. 44

  3. 33

  4. 49
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using weighted average: (2*50 + 3*40) / (2+3) = (100 + 120) / 5 = 220/5 = 44. With 2 boys and 3 girls, the boys contribute 100 and girls contribute 120 to total weight, divided by 5 students gives 44.

Multiple choice

The average weight of 25 students of a class is 28 kg. When 10 new students are admitted, the average increases by 2 kg. Find the average weight of the new students.

  1. 34 kg

  2. 36 kg

  3. 35 kg

  4. 33 kg

  5. 32 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Original number of students (N) = 25

Original average weight (A) = 28 kg

Number of new students (n) = 10 

Difference between the average weights (d) = 2 kg

Now, apply this shortcut formula:

Average weight of new students = A + (N/n + 1)d

= 28 + (25/10 + 1)2

= 35 kg

So, the average weight of 10 new students is 35 kg.

Multiple choice

When a man weighing 75 kg is replaced by another man in a group of 20 persons, the average weight decreases by 2 kg. What is the weight of the new man?

  1. 30 kg

  2. 32 kg

  3. 34 kg

  4. 35 kg

  5. 31 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the shortcut formula:

Weight of the new man - weight of the removed man = NX 

Where, N = number of men in the group and X = increase or decrease in average 

Weight of the new man - 75 = 20(-2)

Weight of the new man = 75 - 40

= 35 kg

Multiple choice

The average salary of 25 teachers is Rs. 6050 per month. Five teachers leave the school and the average salary of the remaining teachers is dropped by Rs. 250. Find the total salary of the teachers who left the school.

  1. Rs. 35250

  2. Rs. 35200

  3. Rs. 35000

  4. Rs. 35300

  5. Rs. 35400
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original number of teachers (N) = 25 

Original average salary (A) = Rs. 6050 

Number of teachers who left the school (n) = 5

Difference between the average salaries (d) = Rs. 250 

Now, apply the following shortcut formula to find the average salary of teachers who left the school:

Average salary of the teachers who left the school = A - (1 - N/n)d

= 6050 - (1 - 25/5) * 250 

= Rs. 7050 

Now, total salary of 5 teachers = 5 * 7050

= Rs. 35250

Multiple choice

The average weight of 31 students in a class is 40 kg. If the weight of the teacher is included, the average weight increases by 0.25 kg. Find the weight of the teacher.

  1. 52 kg

  2. 48 kg

  3. 50 kg

  4. 55 kg

  5. 53 kg
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original average weight of (A) = 46 kg

Original number of candidates (N) = 31

Increase in average weight (d) = 0.25 kg

Now, apply the following shortcut formula:

Weight of the teacher = A + (N + 1 )d

= 46 + (31 + 1) * 0.25 

= 48 kg

Multiple choice

The average age of 41 students of a class is 15 years. When one boy leaves the class, the average is reduced by 0.05 year. Find the age of the boy who left the class.

  1. 13 years

  2. 14 years

  3. 17 years

  4. 16 years

  5. 15 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Original average age (A) = 15 years

Original number of students (N) = 41

Difference in average ages (d) = 0.05 years

Now, apply the shortcut formula:

Age of the boy who left the class = A - (1 - N)d 

= 15 - (1 - 41) * 0.05 

= 17 years 

So, the age of the boy who left the class was 17 years.

Multiple choice

The average of 15 numbers is 26.2. If the average of first 8 numbers is 27.875 and the average of last 8 numbers is 25.125, then find the 8th number.

  1. 31

  2. 28

  3. 23

  4. 29

  5. 27
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average of 15 numbers = 26.2

Then, sum of all 15 numbers = 26.2 * 15

= 393 

Now, average of first 8 numbers = 27.875 

So, sum of first 8 numbers = 27.875 * 8

= 223

And average of last 8 numbers = 25.125 

Then, sum of last 8 numbers = 25.125 * 8

= 201 

So, 8th number = 203 + 201 - 393

= 424 - 393

= 31

Multiple choice

Five years ago, the average age of A and B was 11 years. After adding the age of C to the ages of A and B, the average remained the same. How old is C now?

  1. 14 years

  2. 18 years

  3. 11 years

  4. 16 years

  5. 13 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Five years ago, average age of A and B = 11 years So, sum of ages of A and B, 5 years ago = 11 x 2 = 22 years On adding the age of C, average age of A, B and C = 11 years So, (22 + C)/3 = 11 22 + C = 33 C = 11 Therefore, 5 years ago, C's age was 11 years. So, present age of C = 11 + 5 = 16 years

Multiple choice

The average of the marks secured by 30 students of Grade A is 50, that of 40 students of Grade B is 30 and that of 45 students of Grade C is 55. What is the combined average of the students of the three grades?

  1. 49.28

  2. 45

  3. 43.26

  4. 1725

  5. 38.33
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

It is a correct answer.

Solution  = (30*50 + 40*30 + 45*55) / (30+40+45)                  =(1500 + 1200 + 2475) / 115                  =5175/115                  =45