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

Average age of a group is 28 years. A person aged 26 leaves the group and two persons of age 29 and 32 join the group. If the new average age of the group is 29, then how many members were in the group initialy?

  1. 5

  2. 6

  3. 7

  4. 8

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

Let the initial number of members be m. Then total age of the group = 28 * m Now, new total age of the group = 28 * m + 35 Total number of members after these changes = m + 1 So, (28 m + 35)/(m + 1) = 29  m = 6

Multiple choice

There are 30 students in a class. The average age of the first 10 students is 13.5 years. The average age of the next 20 students is 14.1 years. What is the average age of the whole class?

  1. 13.0 years

  2. 13.5 years

  3. 13.7 years

  4. 13.9 years

  5. 13.8 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total age of 10 students = 13.5 * 10 = 135 years. Total age of 20 students = 14.1 * 20 = 282 years. Average age of 30 students = (135 + 282)/30 = 13.9 years Therefore, it is the correct answer.

Multiple choice

In Arun's opinion, his weight is greater than 65 kg, but less than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg, but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, then what is the average of different probable weights of Arun?

  1. 67 kg

  2. 68 kg

  3. 69 kg

  4. 66.5 kg

  5. 65.5 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Arun's weight be X kg. According to Arun, 65 < X < 72 According to Arun's brother, 60 < X < 70 According to Arun's mother, X <= 68 The values satisfying all the above conditions are 66, 67 and 68. Required average = ( 66 + 67 + 68)/3 = 201/3 = 67 kg

Multiple choice

If 25 persons went to a Barbeque Nation for a combined dinner party and 10 of them spent Rs. 84 each on their dinner and the rest spent Rs. 4 more than the average expenditure of all the 25, then what was the approximate total money spent by them?

  1. Rs. 90

  2. Rs. 2250

  3. Rs. 2225

  4. Rs. 2100

  5. Rs. 1500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Assume x is the average expenditure of 25 people. Then, 25*x = 10*84 + 15 (x + 4)  10*x = 900; x = 90. Thus the total expenditure is 90*25 = 2250.

Multiple choice

The average marks of 28 students in math were 50. When 8 students left the school, then the average increased by 5. What is the average of marks obtained by the students who left?

  1. 37.5

  2. 12.5

  3. 17.5

  4. 39.3

  5. 300
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total marks of 28 students is 28*50 = 1400. After leaving of 8 students total marks is 20*55 = 1100. Decrease in total marks is 1400-1100 = 300. This decrement is the total marks of 8 students who left the class. Thus average is 300/8 = 37.5

Multiple choice

The average weight of 3 persons Kora, Tanzin and Zuko is 90 kg. Another man Bumi joins the group and the average now becomes 85 kg. If another man Marko, whose weight is 3 kg more than that of Bumi, replaces Kora then the average weight of Tanzin, Zuko, Bumi and Marko becomes 81 kg. The weight of Kora is

  1. 99 kg

  2. 85 kg

  3. 94 kg

  4. 82 kg

  5. 89 kg
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The decrease in the average of three persons is 90 – 85 = 5 kg. Total decrease for three persons is 5 × 3 = 15 kg. The weight of Bumi must be New average – Decrease i.e. 85 – 15 = 70 kg. Marko is weight is 3 kg more i.e. 73 kg replaces Kora and thus the average becomes 81. Now if you compare the four persons with Marko the average decreases by 4, thus the total decrease is 4 × 4 = 16 kg. The new included person Marko must be 16 kg lighter than the person who is excluded i.e. Kora. Thus weight of A is 73 + 16 = 89 kg.

Multiple choice

The average age of a class of 61 students was 18 years 4 months on 1st August. If Sakura, whose age was 19 years 2 months on 1st December, left the school in December, what would be the average age of the class on the following 1st April?

  1. 18 years, 11 months and 27 days

  2. 19 years and 29 days

  3. 18 years, 11 months, 27 days and 21 hours

  4. 18 years, 10 months and 27 days

  5. 18 years, 11 months and 28 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let us assume all the students are there only up to the following April. Their average would have increased by 8 months (August – March) and would have become 19 years.
  On the other hand, the students who left in the October would have been of age 19 years and 6 months (December – March) on 1st April. This means extra 6 months would decrease the average of all. Now these six month time means 180 days, which would be equally reducing the average of all the 60 students by 180/60 = 3 days.  The real average of the class will be 19 years – 3 days = 18 years + 11 months + 27 days