Averages Questions

Multiple choice
  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I < Quantity II मात्रा I < मात्रा II

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  5. Quantity I = Quantity II or relationship cannot be established मात्रा I = मात्रा II या सम्बन्ध स्थापित नहीं किया जा सकता है

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Teacher's age = New average × (n+1) - Old average × n = 15 × 37 - 14 × 36 = 555 - 504 = 51. Quantity II: Professor's age = 35.5 × 20 - 35 × 19 = 710 - 665 = 45. Since 51 > 45, Quantity I > Quantity II.

Multiple choice
  1. 59

  2. 59.5

  3. 60

  4. 60.5

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the combined average, first calculate total marks for each group: 8 × 51 = 408 and 9 × 68 = 612. Add these to get 1020 total marks for all 17 students. Divide 1020 by 17 to get the combined average of 60. This is a weighted average problem where the weights are the number of students in each group.

Multiple choice
  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity II > Quantity I मात्रा II > मात्रा I

  4. Quantity II ≥ Quantity I मात्रा II ≥ मात्रा I

  5. Quantity I = Quantity II or Relation cannot be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता है

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total age = 84 × 13 = 1092 years. Using allegation method: the distance from 13 to 15 (girls' average) is 2, and from 13 to 12 (boys' average) is 1. The ratio of boys to girls is 2:1. With 84 students, this gives 56 boys and 28 girls. Therefore Quantity I (56 boys) > Quantity II (28 girls).

Multiple choice
  1. Any two of the three तीन में से कोई दो

  2. All I, II & III सभी I, II और III

  3. Only I & II केवल I और II

  4. Only II & III केवल II और III

  5. Question cannot be answered even with the information in all the three statements तीनों कथनों में दी गयी जानकारी से भी प्रश्न का उत्तर नहीं दिया जा सकता है |

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total students = 60, average weight = 42 kg. Total weight = 2520 kg. Let b be number of boys, g = 60 - b. From II: Boys' average = 43, total boys weight = 43b. From III: Total girls weight = 1144 kg. Total = 43b + 1144 = 2520, giving b = 32, g = 28. Girls' average = 1144/28 = 40.86 kg. All three statements are needed to solve.

Multiple choice
  1. 50 kg 50 किग्रा.

  2. 60 kg 60 किग्रा.

  3. 75 kg 75 किग्रा.

  4. 90 kg 90 किग्रा.

  5. None of these इनमें से कोई नहीं

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Box 1: 200 kg. Box 3: 200×1.25 = 250 kg. Box 2: 250×1.2 = 300 kg. Box 4: 350 kg (given as 30% lower than Box 5). So Box 5: 350/0.7 = 500 kg. Sorted weights: 200, 250, 300, 350, 500. Four heaviest: 250, 300, 350, 500. Average = (250+300+350+500)/4 = 350 kg. Four lightest: 200, 250, 300, 350. Average = (200+250+300+350)/4 = 275 kg. Difference = 350-275 = 75 kg.

Multiple choice
  1. 15

  2. 16

  3. 12

  4. 14

  5. None of these इनमे से कोई नही

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total age of 75 boys = 75 × 16 = 1200 years. First group: 15 × 18 = 270 years. Second group: 25 × 17.6 = 440 years. Remaining boys = 75 - 15 - 25 = 35. Their total age = 1200 - 270 - 440 = 490. Average age of remaining = 490 ÷ 35 = 14 years.

Multiple choice
  1. 56 years 56 वर्ष

  2. 15 years 15 वर्ष

  3. 17 years 17 वर्ष

  4. 34 years 34 वर्ष

  5. None of these इनमें से कोई नहीं

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total age of 40 students = 40 × 15 = 600 years. When teacher is included, total persons = 41 and new average = 16, so total = 41 × 16 = 656 years. Teacher's age = 656 - 600 = 56 years. The teacher's age adds enough to increase the average by 1 year across all 41 people.

Multiple choice
  1. 21 years and 6 months 21 वर्ष और 6 माह

  2. 22 years 22 वर्ष

  3. 21 years 21 वर्ष

  4. 20 years 20 वर्ष

  5. 20 years and 9 months 20 वर्ष और 9 माह

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total age of 80 students = 80 × 19.25 = 1540 years. After 20 leave, 60 students have total age 60 × 19 = 1140 years. The 20 who left had total age 1540-1140=400 years, so average = 400÷20=20 years. Option C (21 years) is a common error from incorrect subtraction.

Multiple choice
  1. 47

  2. 49

  3. 51

  4. 53

  5. None of these इनमें से कोई नहीं

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total weight initially = 24 × 47.25 = 1134 kg. After 2 leave: 22 × 47 = 1034 kg. Weight of both who left = 1134 - 1034 = 100 kg. If one is 49 kg, the other is 100 - 49 = 51 kg.

Multiple choice
  1. 51.472 kg.

  2. 52.152 kg.

  3. 52.882 kg.

  4. 53.072 kg.

  5. 54.702 kg.

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total of 7 experiments: 53.735×7=376.145. First 3 experiments: 54.005×3=162.015. Let 6th and 7th average = 54.005-0.010=53.995, so their sum=107.99. Let 5th experiment = x, then 4th = x+0.004. Sum equation: 162.015 + (x+0.004) + x + 107.99 = 376.145. Solving: 2x + 270.009 = 376.145, so 2x=106.136, giving x=53.068. Fourth experiment: 53.068+0.004=53.072. ✓

Multiple choice
  1. Only III केवल III

  2. All of the necessary सभी आवश्यक है

  3. Only II and III केवल II और III

  4. Only I and II केवल I और II

  5. None of the above इनमे से कोई नहीं

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find overall average weight, we need: average weight of boys (55 kg from I), average weight of girls (49 kg from II), and the relationship between their counts (boys are 30% more than girls from III, so if girls = G, boys = 1.3G). Overall average = (55×1.3G + 49×G) / (1.3G + G) = (71.5G + 49G) / 2.3G = 120.5/2.3 ≈ 52.4 kg. All three statements are necessary.

Multiple choice
  1. 396

  2. 400

  3. 408

  4. 416

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let n be the number of students. Total age of students = 6n. Total age of 12 teachers = 12 × 40 = 480. Combined average: (6n + 480) / (n + 12) = 7. Solving: 6n + 480 = 7n + 84, so n = 396. Option A is correct.

Multiple choice
  1. 30

  2. 31

  3. 32

  4. 33

  5. 34

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total weight of 40 students = 40 × 32 = 1280. Excluding heaviest (H) and lightest (L), 38 students average 31, so their total = 38 × 31 = 1178. Therefore H + L = 1280 - 1178 = 102. When only H is excluded, 39 students average 31, so their total = 39 × 31 = 1209. Therefore H = 1280 - 1209 = 71. When both H and L excluded, 38 students total = 1178. So H + L = 1280 - 1178 = 102. Since H = 71, L = 102 - 71 = 31.

Multiple choice
  1. $44, 22, 11$
  2. $88, 44, 22$
  3. $40, 20, 10$
  4. $133, 66, 33$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the three numbers be x, y, z. Given: x + y + z = 77 x 3 = 231. Also x = 2y and y = 2z, so x = 4z. Substituting: 4z + 2z + z = 231, so 7z = 231, z = 33. Then y = 2 x 33 = 66, and x = 4 x 33 = 132. The numbers are 132, 66, 33.