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

The average age of a group of 10 students is 15 years. When 5 more students join the group, the average age increases by 1 year. The average age of the new students is?
  1. $45$
  2. $20$
  3. $18$
  4. $90$

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Original total age = 10 × 15 = 150 years. New total = 15 × 16 = 240 years. Sum of new students' ages = 240 - 150 = 90 years. Average age of 5 new students = 90 ÷ 5 = 18 years. The average increases because the new students are older than the original average.

Multiple choice

The average weight of M,N,O and P is 44 kg. A new person Q is also included in the group, then the average weight of the group is increased by 1 kg. Again a new person R is replaced M. Then the new average of 5 person becomes 46 kg. what is the average weight of N,O,P and R ?

  1. 44.25 kg
    1. 75 kg

  3. 45.25 kg

  4. 43.75 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

M+N+O+P = 44 × 4 = 176 kg. Adding Q: average increases by 1 kg, so new average = 45 kg for 5 people. Total with Q = 45 × 5 = 225 kg. Q's weight = 225 - 176 = 49 kg. Replacing M with R: new average of 5 people = 46 kg. Total = 46 × 5 = 230 kg. Since Q stays, weight of (N+O+P+R) = 230 - 49 = 181 kg. Average of N,O,P,R = 181/4 = 45.25 kg.

Multiple choice

The average age of 120 members of a society is 62.5 years. On adding 30 new members, the average age becomes 58.2 years, what is the average age of the newly added members?

  1. 40 years

  2. 41 years

  3. 39 years

  4. 42 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total age of 120 members = 120 × 62.5 = 7500 years. After adding 30 members, total members = 150 and new total age = 150 × 58.2 = 8730 years. Age of 30 new members = 8730 - 7500 = 1230 years. Average age of new members = 1230/30 = 41 years. This is a weighted average problem where the new group has lower age, pulling down the overall average.

Multiple choice

In a hotel, there are 120 staff members. Their average weight is 62.5kg . When one of the staff members leaves the hotel, the average weight is reduced by 250 g. Find the weight of the staff member who left the hotel.

  1. 64.25 kg

  2. 78.75 kg

  3. 90.50 kg

  4. 92.25 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Original total weight = 120×62.5 = 7500 kg. New average = 62.5-0.25 = 62.25 kg. New total = 119×62.25 = 7407.75 kg. Weight of person who left = 7500-7407.75 = 92.25 kg. Option D is correct. Option A(64.25), B(78.75), and C(90.50) don't match the calculated weight.

Multiple choice

The average weight of some students in a class was 69.5 kg. When 10 students of average weight 68 kg joined the class, and 6 students of average weight 60 kg left the class, it was noted that the average weight of the new group of students increased by 2 kg. How many students are there in the class now? एक कक्षा में कुछ विद्यार्थियों का औसत भार 69.5 किग्रा था। जब 68 किग्रा के औसत वजन वाले 10 छात्र कक्षा में शामिल हुए और 60 किग्रा के औसत वजन के 6 छात्रों ने कक्षा छोड़ दी, तो यह देखा गया कि छात्रों के नए समूह के औसत वजन में 2 किग्रा की वृद्धि हुई। अब कक्षा में कितने विद्यार्थी हैं?

  1. 12

  2. 21

  3. 23

  4. 17

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be original students. Total weight = 69.5n. After 10 join (avg 68kg) and 6 leave (avg 60kg), new count = n+4 and new avg = 71.5kg. Equation: 69.5n + 10×68 - 6×60 = 71.5(n+4). Solving: 69.5n + 320 = 71.5n + 286, so 2n = 34, n = 17. Current students = 17+4 = 21. Option B is correct. Option A doesn't account for all changes, C and D are calculation errors.

Multiple choice

The average weight of 49 students in a class is 49 kg. Seven of them whose average weight is 50 kg leave the class and other seven students whose average weight is 64 kg join the class. What is the new average weight (in kg) of the class? एक कक्षा में 49 विद्यार्थियों का औसत भार 49 किग्रा है। उनमें से सात जिनका औसत वजन 50 किग्रा है, कक्षा छोड़ देते हैं और अन्य सात छात्र जिनका औसत वजन 64 किग्रा है, कक्षा में शामिल हो जाते हैं। कक्षा का नया औसत वजन (किग्रा में) क्या है?

  1. 51

  2. 48

  3. 50

  4. 52

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial total weight = 49 students × 49 kg = 2401 kg. Weight of 7 leaving students = 7 × 50 = 350 kg. Weight of 7 joining students = 7 × 64 = 448 kg. New total = 2401 - 350 + 448 = 2499 kg. New average = 2499 ÷ 49 = 51 kg. The number of students remains 49, so we only need to adjust the total weight.

Multiple choice

The total marks obtained by Rani in Physics, Chemistry and Mathematics is 130 more than the marks obtained by her in Chemistry. What is the average marks obtained by her in Physics and Mathematics together?

  1. 65

  2. 60

  3. 55

  4. 50
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let P, C, M be marks in Physics, Chemistry, and Mathematics. The statement means P + C + M = C + 130. Cancel C from both sides to get P + M = 130. The average of Physics and Mathematics marks is (P + M)/2 = 130/2 = 65.

Multiple choice

In an examination, average marks of a student per paper were 61. If he would have obtained 19 more marks in english; 13 more marks in hindi and 8 more marks in maths, his average marks per paper would have been 66. How many papers were there in the examination?

  1. 5

  2. 6

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let n be the number of papers. Total marks = 61n. After bonus marks, total = 61n + 19 + 13 + 8 = 61n + 40. New average = (61n + 40)/n = 66. Solving: 61 + 40/n = 66, so 40/n = 5, giving n = 8. There were 8 papers in the examination.

Multiple choice

The average marks obtained by 80 students in an examination is 50. If the average marks of passed students is 55 and the number of students who failed the examination are 30, then what is the average marks of students who failed the examination?

  1. 41.66

  2. 46.66

  3. 40.33

  4. 52.33
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total marks for 80 students = 80 × 50 = 4000. If 30 failed, then 50 passed with average 55, contributing 50 × 55 = 2750 marks. The remaining 1250 marks are from 30 failed students, so their average is 1250 ÷ 30 = 41.67 (approximately 41.66). This is a weighted average problem where you balance the total against known subgroups.

Multiple choice

The heights of six people are given as 6 feet 6 inches, 6 feet, 5 feet 8 inches, 6 feet 2 inches, 6 feet 4 inches, and 5 feet 10 inches, respectively. Find the average height of these six people?

  1. 6 feet 4 inch

  2. 6 feet

  3. 6 feet 1 inch

  4. 6 feet 6 inch
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Convert all heights to inches: 6'6" = 78", 6' = 72", 5'8" = 68", 6'2" = 74", 6'4" = 76", 5'10" = 70". Sum = 78+72+68+74+76+70 = 438 inches. Average = 438÷6 = 73 inches = 6 feet 1 inch.

Multiple choice

The average of the marks of 25 students in a class, in an examination was calculated to be 19. Later, the teacher realized that the marks of two students were taken as 18 and 19 respectively, instead of 14 and 15 . Find the actual average marks of the class.

  1. 17.43

  2. 16.56

  3. 18.68

  4. 17.65
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The original total marks were 25 × 19 = 475. The error is the difference between the wrongly recorded marks (18+19=37) and the actual marks (14+15=29), which is 8 marks too high. Correct total = 475 - 8 = 467. Actual average = 467/25 = 18.68.

Multiple choice

In a company average age of female employees is 24 years. Average age of all the employees is 32 years. If number of male and female is same, then what will be the average age of male employees?

  1. 40 years

  2. 42 years

  3. 48 years

  4. 38 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the number of male and female employees each be n. Total age of females = 24n. Total age of all employees = 32 × 2n = 64n. Total age of males = 64n - 24n = 40n. Average age of males = 40n/n = 40 years.

Multiple choice

Average weight of 20 persons is 60 kg. A new person joins the group and average weight of 21 persons becomes 59 kg. What will be the weight of the new person?

  1. 41 kg

  2. 29 kg

  3. 39 kg

  4. 40 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total weight of 20 persons = 20 × 60 = 1200 kg. Total weight of 21 persons = 21 × 59 = 1239 kg. The new person's weight = 1239 - 1200 = 39 kg. Option B (29 kg) and D (40 kg) are incorrect as they don't match the calculated difference.

Multiple choice

The average weight of 18 persons increases by 2.5 kg when a new person comes in place of one of them weighing 72 kg. The weight of the new person is:

  1. 107 kg

  2. 127 kg

  3. 117 kg

  4. 77 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The average weight of 18 persons increases by 2.5 kg. Total increase = 18 × 2.5 = 45 kg. This increase comes from replacing a 72 kg person with the new person. So new person's weight = 72 + 45 = 117 kg. The average increases because the new person is heavier than the person they replaced.