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

Ram was given the task to calculate the average marks of ten students of the class. It was known that none of the students scored less than 10 or more than 100 marks. By mistake, Ram interchanged the two digits of the marks of Shyam. As a result, the average of marks calculated for the ten students were 2.7 more than what it would have been. What could be positive difference of the digits of the marks of Shyam?

  1. 1

  2. 2

  3. 3

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

Let the marks be 10x + y. Interchanging gives 10y + x. The difference in marks is |(10y+x) - (10x+y)| = |9(y-x)|. The average difference is 2.7, so the total sum difference is 2.7 * 10 = 27. Thus, 9|y-x| = 27, which means |y-x| = 3.

Multiple choice

A surprise test was conducted in a class of 21 students and the average marks obtained by 21 students were 45. Out of this, the average marks obtained by first 10 students were 42 while last 10 students obtained 43. What is the marks obtained by the 11th student in the class?

  1. 80

  2. 95

  3. 96

  4. 97
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total marks = 21 * 45 = 945. First 10 = 10 * 42 = 420. Last 10 = 10 * 43 = 430. 11th student = 945 - (420 + 430) = 945 - 850 = 95.

Multiple choice

In a village, total number of people is 125 (excluding children). Their average income is Rs. 9500. Out of which, the average income of 65 people is Rs. 6500 and that of 50 other is around Rs. 7000. Find the mean or average income of the rest of the people.

  1. Rs. 40,500

  2. Rs. 41,500

  3. Rs. 43,000

  4. Rs. 44,000

  5. Rs. 56,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total income is 125 * 9500 = 1,187,500. Income of 65 people is 65 * 6500 = 422,500. Income of 50 people is 50 * 7000 = 350,000. The remaining 10 people (125 - 65 - 50) have a total income of 1,187,500 - 422,500 - 350,000 = 415,000. The average income of the rest is 415,000 / 10 = 41,500.

Multiple choice

During the mid-semester exams, Navdeep scored 70% marks in English out of 240. She wants to increase her overall average to 80%. How much marks should she score in Mathematics out of 180?

  1. 90%

  2. 93.33%

  3. 94.33%

  4. 95.33%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total marks for 240 + 180 = 420. Target average 80% means total marks = 0.8 * 420 = 336. Marks in English = 0.7 * 240 = 168. Marks needed in Math = 336 - 168 = 168. Percentage in Math = (168 / 180) * 100 = 93.33%.

Multiple choice

During his weekly tests, Mohan's average was 85 in 7 subjects. Out of these, the difference between the highest marks and the second highest marks is equal to the difference between the second highest marks and the third highest marks, and it is equal to 5. If we eliminate these three subjects, the average marks become 76. What is the highest score of Mohan?

  1. 89

  2. 90

  3. 92

  4. 102
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the marks be x, x-5, x-10. Sum of 7 subjects = 7 * 85 = 595. Sum of remaining 4 subjects = 4 * 76 = 304. Sum of top 3 = 595 - 304 = 291. x + x-5 + x-10 = 291 => 3x = 306 => x = 102.

Multiple choice

Gaurav has scored 40% marks in English out of a total of 200 marks, during the mid-semester exams. How much marks should he score out of a total of 150 marks to get an overall average of 50% in both of the exams?

  1. 59.42%

  2. 60%

  3. 63.33%

  4. 64.36%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total marks = 200 + 150 = 350. Required average = 50% of 350 = 175. Marks in English = 40% of 200 = 80. Marks needed in second exam = 175 - 80 = 95. Percentage = (95 / 150) * 100 = 63.33%.

Multiple choice

When a person weighing 80 kg left a bus, the average weight of the remaining 39 travelers is increased by 100 g. What is the average weight of the remaining 39 travelers?

  1. 80 kg

  2. 82 kg

  3. 84 kg

  4. 86 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial average be A for 40 people. Total weight = 40A. After 80kg leaves, total weight = 40A - 80. New average = (40A - 80) / 39 = A + 0.1. 40A - 80 = 39A + 3.9. A = 83.9. The new average is 83.9 + 0.1 = 84 kg.

Multiple choice

The average weight of sugar bags was 50 kg. Later, it was found that due to some technical error in weighing scale, the 100 bags which were weighing 90 kg, had an actual weight of 60 kg each which dropped the average weight of all the bags to 45 kg. Calculate the total number of sugar bags.

  1. 150

  2. 250

  3. 600

  4. 650
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let N be the total bags. Initial total weight = 50N. New total weight = 50N - 100*(90-60) = 50N - 3000. New average = 45, so (50N - 3000)/N = 45. 50N - 3000 = 45N, 5N = 3000, N = 600.

Multiple choice

In a science experiment which was done 10 times, an intern calculated the average of all the readings and he noticed that all the readings are in 2 digits. After cross checking, his professor found out that reading digits are interchanged due to which average is 1.8 less than the exact value. Calculate the difference of the digits of the numbers in which he made a mistake.

  1. 2

  2. 3

  3. 4

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the two-digit number be 10x + y. Interchanging digits gives 10y + x. The difference is (10x + y) - (10y + x) = 9(x - y). Since the average of 10 readings changed by 1.8, the total sum changed by 10 * 1.8 = 18. Thus, 9(x - y) = 18, which means x - y = 2.

Multiple choice

The average marks obtained by a student in some tests is 15. On re-appearing for first and last test, his score improved in first test by 30 but it reduced by 5 marks in last test. Due to which, his average improved and became 17.5. Find the total number of tests in which he appeared.

  1. 20

  2. 18

  3. 15

  4. 10
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let n be the number of tests. Initial sum = 15n. New sum = 15n + 30 - 5 = 15n + 25. New average = (15n + 25)/n = 17.5. 15n + 25 = 17.5n, so 2.5n = 25, n = 10.

Multiple choice

Directions: In the following question, we have two quantities given. Compare these quantities and answer accordingly with the following given options. (a) Quantity I > Quantity II (b) Quantity I < Quantity II (c) Quantity I ≥ Quantity II (d) Quantity I ≤ Quantity II (e) Quantity I = Quantity II or No relation Quantity I: The average weight of 10 girls in a class is 40 kg. If one girl left the class, then the average weight of all the girls decreases by 2. Then the weight of girl who left the class. Quantity II: 48 kg

  1. a

  2. b

  3. c

  4. d

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

Total weight of 10 girls = 10 * 40 = 400 kg. After one girl leaves, 9 girls remain with an average of 40 - 2 = 38 kg. Total weight of 9 girls = 9 * 38 = 342 kg. Weight of the girl who left = 400 - 342 = 58 kg. Since 58 > 48, Quantity I > Quantity II.