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

A man bought a 8 shirts as Rs. 50 each and 15 pants at Rs. 60 each and 12 pairs of shoes at Rs. 65 a pair. Find the average value of articles. एक आदमी ने 8 शर्ट प्रत्येक 50 रू. की दर से खरीदी और 15 पैन्ट प्रत्येक 60 रू. की दर से और 12 जोड़े जूते प्रत्येक 65 रू. के जोड़े की दर से खरीदे तो वस्तु का औसत मूल्य क्या है?

  1. Rs. 48.25

  2. Rs. 60.00

  3. Rs. 59.42

  4. Rs. 32.00
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total cost = 8*50 + 15*60 + 12*65 = 400 + 900 + 780 = 2080. Total articles = 8 + 15 + 12 = 35. Average = 2080/35 = 59.428... ≈ Rs. 59.42. Option C is correct.

Multiple choice

The average age of A and B, 2 years ago was 26 years. If the age of A, 5 years hence will be 40 years, and B is 5 years younger than C, then find the difference between the age of A and C.

  1. 6

  2. 9

  3. 7

  4. 8

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

2 years ago, average age of A and B was 26, so their combined age was 52. Currently: A + B = 52 + 4 = 56. A's age 5 years hence = 40, so A's current age = 35. Therefore B = 56 - 35 = 21. B is 5 years younger than C, so C = 21 + 5 = 26. Difference between A and C = 35 - 26 = 9.

Multiple choice

What is the age of class teacher? I. There are 11 students in the class. II. The average age of students and class teacher is 14 years. III. The average age of students and teacher is 3 years more than the average age of the students.

  1. I and III

  2. I and II

  3. II and either I or III

  4. All

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

Let average age of 11 students be S. Total students age = 11S. From III: (11S+T)/12 = S+3, so 11S+T = 12S+36, giving T = S+36. From II: (11S+T)/12 = 14, so 11S+T = 168. Substituting T: 11S+(S+36) = 168, so 12S = 132, S = 11. Therefore T = 11+36 = 47 years. All three statements are needed.

Multiple choice

Find the value of quantities and state the correct relationship. Quantity I: A man on tour travels first 160 km at 64 km/hr. and the next 160 km at 80 km/hr. Find the average speed of the tour. Quantity II: A went from P to Q with the speed of 60km/hr. and return back with the speed of 90km/hr. Find the average speed.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I Quantity II

  5. Quantity I = Quantity II or no relation can be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: Total distance = 320 km, total time = 160/64 + 160/80 = 2.5 + 2 = 4.5 hours. Average speed = 320/4.5 = 71.11 km/hr. Quantity II: Average speed for round trip = 2×60×90/(60+90) = 72 km/hr. Therefore Quantity I (71.11) < Quantity II (72).

Multiple choice

Find the value of both quantities and state the correct relationship. Quantity I: Marks of new student, if the average marks of 25 students is 55 and after the marks of new student also taken into consideration, average increases by 2 marks Quantity II: Marks of new student, if the average marks of 20 students is 80 and after the marks of new student also taken into consideration, average increases by 1.5 marks

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Total marks of 25 students = 25 × 55 = 1375. After adding new student, average becomes 57, so total = 26 × 57 = 1482. New student's marks = 1482 - 1375 = 107. Quantity II: Total marks of 20 students = 20 × 80 = 1600. After adding new student, average becomes 81.5, so total = 21 × 81.5 = 1711.5. New student's marks = 1711.5 - 1600 = 111.5. Clearly 111.5 > 107, so Quantity II is greater.

Multiple choice

The average marks of five subjects is 27 out of 30. If one subject's marks is excluded, the average becomes 25. The marks in the excluded subject is

  1. 25

  2. 27

  3. 30

  4. 35
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total marks for 5 subjects = 27 × 5 = 135. After excluding one subject, 4 subjects have average 25, so their total = 25 × 4 = 100. The excluded subject = 135 - 100 = 35. Common mistake: assuming the excluded subject equals the old average (27) or new average (25).

Multiple choice

In a school with 600 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years 9 months, then the number of boys in the school is

  1. 150

  2. 250

  3. 350

  4. 450
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x boys, y girls. x + y = 600. Average age = 11 years 9 months = 11.75 years. So (12x + 11y) / 600 = 11.75. Substituting y = 600 - x: 12x + 11(600 - x) = 7050, so x + 6600 = 7050, x = 450 boys. Option D is correct.

Multiple choice

The average age of 80 boys in a class is 19 years. The average age of a group of 15 boys in the class is 21 years and the average age of another group of 25 boys in the class is 18 years. What is the average age of the remaining boys in the class? कक्षा में 80 लड़कों की औसत आयु 19 वर्ष है। कक्षा में 15 लड़कों के एक समूह की औसत आयु 21 वर्ष है और कक्षा में 25 लड़कों के दूसरे समूह की औसत आयु 18 वर्ष है। कक्षा में शेष लड़कों की औसत आयु क्या है?

  1. 18.5 years/वर्ष

  2. 17.5 years/वर्ष

  3. 18.875 years/वर्ष

  4. 19.25 years/वर्ष
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total age of 80 boys = 80 × 19 = 1520 years. Age of first 15 boys = 15 × 21 = 315 years. Age of next 25 boys = 25 × 18 = 450 years. Remaining boys = 80 - 15 - 25 = 40. Their total age = 1520 - 315 - 450 = 755 years. Average age = 755/40 = 18.875 years. The claimed answer is correct.

Multiple choice

The average weight of 29 students is 40 kg. If the weight of teacher be included the average weight is increased by 300 gms. The weight of the teacher is- 29 छात्रों का औसत भार 40 किग्रा है। यदि अध्यापक का भार सम्मिलित कर लिया जाए तो औसत भार 300 ग्राम बढ़ जाता है। अध्यापक का भार है-

  1. 49

  2. 56

  3. 58

  4. 53
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total weight of 29 students = 29 × 40 = 1160 kg. New average with teacher = 40 + 0.3 = 40.3 kg. Total weight of 30 people = 30 × 40.3 = 1209 kg. Teacher's weight = 1209 - 1160 = 49 kg. Option A is correct.

Multiple choice

The average temperature for Monday, Tuesday and Wednesday was (40^oC). The average for Tuesday, Wednesday and Thursday was (41^oC). If the temperature on Thursday be (42^oC), Find the temperature on Monday.
  1. $\(39^oC\)$
  2. $\(40^oC\)$
  3. $\(43^oC\)$
  4. $\(38^oC\)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M, Tu, W, Th be temperatures. M + Tu + W = 3×40 = 120. Tu + W + Th = 3×41 = 123. Given Th = 42. From second equation: Tu + W = 123 - 42 = 81. Substitute in first: M + 81 = 120, so M = 39°C. However, option A says 39°C. Wait - let me verify: 120 - 81 = 39. This matches A. But earlier I calculated 37. Recomputing carefully: Tu + W = 81, M = 120 - 81 = 39. The answer 39°C matches option A. My earlier calculation of 37°C was incorrect.

Multiple choice

The average of 10 numbers is 17.3. If the average of first five numbers is 14.2 and the average of last six numbers is 19.4. What is the fifth number?

  1. 14.4

  2. 12

  3. 13.8

  4. 17.8

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

Sum of 10 numbers = 10×17.3 = 173. Sum of first 5 = 5×14.2 = 71. Sum of last 6 = 6×19.4 = 116.4. The 5th number is counted in both first-5 and last-6 groups. So 71 + 116.4 - 5th = 173, 5th = 187.4 - 173 = 14.4. Answer A is correct.

Multiple choice

If the average marks of 1/5 th class is 80% and that of and that of 1/4 th class is 75% and the average marks of the rest class is 65%, then what is the average of the whole class? यदि कक्षा के 1/5 भाग के औसत अंक 80% है और 1/4 भाग का औसत 75% है और शेष भाग का औसत अंक 65% है, तो पूरी कक्षा का औसत क्या है?

  1. 60

  2. 70.5

  3. 75

  4. 58
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total students = n. 1/5n students score 80%, 1/4n score 75%, rest (n - n/5 - n/4 = 11n/20) score 65%. Total marks = (n/5)*80 + (n/4)*75 + (11n/20)*65 = 16n + 18.75n + 35.75n = 70.5n. Average = 70.5n/n = 70.5. The weighted average accounts for different group sizes.

Multiple choice

If we consider four numbers, the average of first three is 18 and that of last three is 19. If the last number is 16, find the first number. यदि हम चार संख्याओं पर विचार करते हैं, तो पहले तीन का औसत 18 है और अंतिम तीन का औसत 19 है। यदि अंतिम संख्या 16 है, तो पहली संख्या ज्ञात कीजिये।

  1. 13

  2. 15

  3. 11

  4. 14
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let numbers be a, b, c, d. Average of first three: (a+b+c)/3 = 18, so a+b+c = 54. Average of last three: (b+c+d)/3 = 19, so b+c+d = 57. Given d=16, so b+c = 57-16 = 41. Then a = 54 - (b+c) = 54 - 41 = 13. The key is using both equations to eliminate b+c.

Multiple choice

Find the value of quantities and state the correct relationship.\newline In a container there are 20 eggs out of which 5 are rotten. Two eggs are chosen at random.\newline Quantity I: Probability that at least one egg is rotten\newline Quantity II: Average of (\frac{1}{2}), (\frac{1}{3}) and (\frac{1}{5})

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Probability at least one rotten = 1 - P(both good) = 1 - (15C2/20C2) = 1 - (105/190) = 85/190 = 17/38 ≈ 0.447. Quantity II: Average of 1/2, 1/3, 1/5 = (1/2 + 1/3 + 1/5)/3 = (15/30 + 10/30 + 6/30)/3 = (31/30)/3 = 31/90 ≈ 0.344. Since 17/38 > 31/90, Quantity I > Quantity II.