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 of 10 numbers is 40.2. Later it is found that two numbers have been wrongly added. The first is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
  1. $40.2$
  2. $40.4$
  3. $40.6$
  4. $40.8$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original sum = 10 * 40.2 = 402. First error: added number that was 18 greater than actual. This increased sum by 18. Second error: added 13 instead of 31. This decreased sum by 31-13 = 18. Net change in sum: +18 - 18 = 0. Therefore correct sum = 402, and correct average = 402/10 = 40.2. The errors cancel out exactly.

Multiple choice

The average age of a family of five members is 24. If the youngest member of the family is 8 years old, then find the average of the family at the time when the youngest member was born?

  1. 20

  2. 24

  3. 16

  4. 23

  5. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Current total age of 5 members = 5 × 24 = 120 years. Youngest is 8 years old. When the youngest was born (8 years ago), the other 4 members were each 8 years younger. Their total age then was 120 - 8 - (4 × 8) = 80 years. Including the newborn (age 0), there were 5 family members. Average = 80 ÷ 5 = 16 years.

Multiple choice

The average age of a class is 12.05 years. The average age of all girls is 12.5 years and average age of all boys is 11.75 years. If total number of boys is 45, what is the total number of girls?

  1. 20

  2. 25

  3. 30

  4. 35

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

Using weighted average formula: Total avg = (Boys × Boy avg + Girls × Girl avg) / (Boys + Girls). Let g = number of girls. 12.05 = (45 × 11.75 + g × 12.5) / (45 + g). Solving: 12.05(45 + g) = 528.75 + 12.5g, 542.25 + 12.05g = 528.75 + 12.5g, 13.5 = 0.45g, g = 30.

Multiple choice

The average weight of M, N and O is equal to 65 Kg. The average weight of M and N is equal to 69.5 kg. The average weight of N and O is 66.5 kg. What is the weight of N in kg?

  1. 70

  2. 73

  3. 75

  4. 77

  5. 80
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let weights be M, N, O. We know: M+N+O=195, M+N=139, N+O=133. Subtract M+N=139 from total: O=56. Subtract N+O=133 from total: M=62. Then N=195-62-56=77. Substitute to verify: M+N=62+77=139 (correct), N+O=77+56=133 (correct).

Multiple choice

In a class there are 25 students whose average age is decreased by 3 months when student aged 22 years is replaced by a new student. Find the age of the new student.

  1. 16 years 4 months

  2. 16 years 7 months

  3. 15 years 4 months

  4. Can't be determined

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

When a student aged 22 years is replaced and the average decreases by 3 months (0.25 years), the new student's age is 22 - (25 × 0.25) = 22 - 6.25 = 15.75 years, which is 15 years and 9 months. The closest option is 16 years 4 months, but it's not exact. The calculation: Average decrease = (Old age - New age) / 25, so New age = 22 - (0.25 × 25) = 15.75 years = 15 years 9 months.

Multiple choice

A librarian purchased 50 story books for his library but he saw that he could get 14 books more by spending Rs. 76 more and per book average becomes Rs. 1 less. The average price (in Rs.) of each book he bought was : एक लाइब्रेरियन अपनी लाइब्रेरी के लिए कहानी की 50 किताबें खरीदता है। लेकिन वह पाता है कि वह 76 और खर्च करके वह 14 किताबें अधिक खरीद सकता है और प्रति किताब औसत मूल्य 1 कम हो जाता है। तो उसके द्वारा खरीदी गयी प्रत्येक किताब का औसत मूल्य ज्ञात करें ?

  1. 10

  2. 12

  3. 9

  4. 13
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let original average price = x. Total cost of 50 books = 50x. New scenario: 64 books with average (x-1), so total cost = 64(x-1) = 50x + 76. Solving: 64x - 64 = 50x + 76, giving 14x = 140, so x = 10. The average price of each book originally bought was Rs. 10.

Multiple choice

The average weight of three men A, B and C is 84 kg. If another person D joins them then average weight of the four men becomes 80 kg. If E whose weight is 3 kg more than that of D, replaces to A, then new average weight of B, C, D and E becomes 79 kg. The weight of A is. तीन व्यक्तियों A, B एवं C का औसत वजन 84 किग्रा. है। यदि एक अन्य व्यक्ति D सम्मिलित होता है तो चार व्यक्तियों का नया औसत वजन 80 किग्रा. हो जाता है। यदि E जिसका वजन D के वजन से 3 किग्रा. अधिक है, A को प्रतिस्थापित करता है तो B, C, D एवं E का नया औसत वजन 79 किग्रा. हो जाता है। A का वजन ज्ञात कीजिए।

  1. 65 kg/किग्रा.

  2. 70 kg/किग्रा.

  3. 75 kg/किग्रा.

  4. 80 kg/किग्रा.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total weight of A+B+C = 3 × 84 = 252 kg. Adding D makes total 4 × 80 = 320 kg, so D = 320 - 252 = 68 kg. E = D + 3 = 71 kg. When E replaces A, average of B,C,D,E = 79, so their total = 316 kg. Total of B+C+D = 316 - 71 = 245 kg. But B+C+D = 252 - A + 68. So 320 - A = 245, giving A = 75 kg.

Multiple choice

The average marks of 24 students of a class in maths is 56. If the marks of three students was mistakenly read as 44, 45 and 61 in place of 48, 59 and 67, then what is the correct average? 24 छात्रों की एक कक्षा के अंग्रेजी विषय के औसत अंक 56 है | यदि तीन विद्यार्थियों के अंक गलती से 44, 45 और 61, जबकि उनके वास्तविक अंक क्रमशः 48, 59 और 67 थे, तो सही औसत कितना होगा ?

  1. 57

  2. 55

  3. 57.5

  4. 58.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Current total marks = 56 × 24 = 1344. The mistaken marks total 44 + 45 + 61 = 150. The correct marks total 48 + 59 + 67 = 174. The difference is 174 - 150 = 24. Correct total = 1344 + 24 = 1368. Correct average = 1368 ÷ 24 = 57.

Multiple choice

The average age of four students is 18.5 years if the age of class-teacher is included with them, then average increases by 20% then what will be the age of class-teacher after 8 years. चार छात्रों की औसत आयु 18.5 वर्ष है यदि उनके साथ कक्षा-अध्यापक की आयु भी शामिल कर ली जाय, तो औसत 20% बढ़ जाता है। तद्नुसार कक्षा अध्यापक की 8 वर्ष बाद आयु कितनी होगी ?

  1. 37 years/वर्ष

  2. 45 years/वर्ष

  3. 43 years/वर्ष

  4. 48 years/वर्ष
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total age of 4 students = 18.5 × 4 = 74 years. New average = 18.5 + 20% of 18.5 = 18.5 + 3.7 = 22.2 years. Total age of 5 people (4 students + teacher) = 22.2 × 5 = 111 years. Teacher's current age = 111 − 74 = 37 years. After 8 years = 37 + 8 = 45 years.

Multiple choice

There are five boxes in a store. The weight of the first box is 200 kg. and the weight of the second box is 20% higher than the weight of the third box whose weight is 25% higher than the first box. The fourth box of 350 kg. is 30% lower than the fifth box. The difference in average weight of the four heaviest boxes and the four lightest boxes is-

  1. 50 kg

  2. 60 kg

  3. 75 kg

  4. 90 kg

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

Box 3 = 125% of 200 = 250 kg. Box 2 = 120% of 250 = 300 kg. Box 4 = 350 kg (given) and is 70% of Box 5, so Box 5 = 350/0.7 = 500 kg. Weights: 200, 250, 300, 350, 500 kg. Average of 4 heaviest (250,300,350,500) = 350 kg. Average of 4 lightest (200,250,300,350) = 275 kg. Difference = 75 kg.

Multiple choice

There are 100 persons in 3 categories A, B and C in a Wrestling competition. The average weight of all the categories was 84. The average of B and C was 87.5 and the average weight of A is 70. The number of persons in A was

  1. 20

  2. 35

  3. 30

  4. 25
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let persons in A be 'a'. Then persons in B+C = (100-a). Total weight = 100 × 84 = 8400. Weight of A = 70a. Weight of B+C = 87.5(100-a) = 8750 - 87.5a. Equation: 70a + 8750 - 87.5a = 8400, giving -17.5a = -350, hence a = 20.

Multiple choice

The average marks of some students in a class is 43. When 4 students are included the average becomes 42.5 and the marks of those 4 students are 42, 36.5, 39 and 42.5. Find the number of student in the class. एक कक्षा में कुछ छात्रों के औसत अंक 43 हैं। जब 4 नये छात्र को शामिल कर लिया जाता हैं तो औसत 42.5 हो जाता है और उन 4 छात्रों के अंक 42, 36.5, 39 और 42.5 है। कक्षा के कुल छात्रों की संख्या ज्ञात कीजिए।

  1. 15

  2. 20

  3. 25

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

Let original number of students be n. Total marks = 43n. After adding 4 students with marks 42, 36.5, 39, 42.5 (total = 160), new average = (43n + 160)/(n + 4) = 42.5. Solving: 43n + 160 = 42.5n + 170, so 0.5n = 10, giving n = 20.