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 travels 60km at the speed 30km/h and next 30km at 15 km/h and 180km at the speed of 90km/h. find his average speed?

  1. 35 km/h

  2. 45 km/h

  3. 55 km/h

  4. 90 km/h

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

Average speed = total distance / total time. Total distance = 60 + 30 + 180 = 270 km. Time for each segment: 60/30 = 2 hr, 30/15 = 2 hr, 180/90 = 2 hr. Total time = 6 hr. Average speed = 270/6 = 45 km/h. The key is that you cannot simply average the speeds (30, 15, 90) because distances are different.

Multiple choice

Jaspreet is going from New Delhi to Amritsar by Car. If he goes at a speed of 40 km./hr. and returns with a speed of (x) km./hr then find the value of (x) if the average speed of the whole journey is 80 km./hr.
  1. $160 km./hr$
  2. $40 km./hr$
  3. $120 km./hr$

  4. Can't be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For equal distances, average speed = 2ab/(a+b), not arithmetic mean. With speeds 40 and x: 2(40)(x)/(40+x) = 80. Solving: 80x/(40+x) = 80, so 80x = 3200 + 80x, giving 0 = 3200, which is impossible. The equation has no solution - an 80 km/hr average is mathematically unattainable when one speed is 40 km/hr.

Multiple choice

In an exam, the average marks obtained by John in English, Maths, Hindi and Drawing were 50. His average marks in Maths, Science, Social Studies and Craft were 70. If the average marks in all seven subjects is 58, his score in maths was?

  1. 50

  2. 52

  3. 60

  4. 74
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M be the math score. First group: E + M + H + D = 200. Second group: M + S + SS + C = 280. All seven subjects: E + M + H + D + S + SS + C = 406. Adding the first two equations and subtracting the third gives 2M = 148, so M = 74. Math is common to both groups, counted twice in the sum.

Multiple choice

There are 50 students in a class. One of them weighing 50 kg goes away and a new student joins. By this the average weight of the class increases by (\frac{1}{2}) kg. The weight of the new student is

  1. 70 kg

  2. 72 kg

  3. 75 kg

  4. 76 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original average be A. Original total = 50A. New total = 50A - 50 + W (where W is new student's weight). New average = A + 0.5. So (50A - 50 + W)/50 = A + 0.5. Solving: 50A - 50 + W = 50A + 25, so W = 75 kg.

Multiple choice

The average age of 20 boys in a class is 12 years. 5 new boys are admitted to the class whose average age is 7 years. The average age of the boys in the class becomes

  1. 8.2 years

  2. 9.5 years

  3. 12.5 years

  4. 11 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total age of 20 boys = 20 × 12 = 240 years. Total age of 5 new boys = 5 × 7 = 35 years. Combined total age = 240 + 35 = 275 years for 25 boys. New average = 275 ÷ 25 = 11 years. This is a weighted average problem where the final average depends on both group sizes.

Multiple choice

A tabulator while calculating the average marks of 100 students of an examination, by mistake enters a student’s marks as 84, instead of 48 and obtained the average as 50; the actual average is-

  1. 49.64

  2. 56.36

  3. 57.64

  4. 53.36
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The incorrect average was calculated with one student's marks as 84 instead of 48, a difference of 36 marks. This excess is distributed among 100 students, so the calculated average exceeds the actual average by 36/100 = 0.36. Therefore, the actual average is 50 - 0.36 = 49.64.

Multiple choice

The average weight of five friends P, Q, R, S, and T is ( (x + 6) ) kg while the average weight of R and T is ( (x – 6) ) kg. If the weight of another person U is also added, then the average weight of all of them is reduced by 5 kg. Find the value of ‘x’ if the average weight of P, Q, S and U is 94.5 kg.

  1. 90

  2. 88

  3. 70

  4. 60
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let P+Q+R+S+T = 5(x+6) = 5x+30. Given R+T = 2(x-6) = 2x-12, so P+Q+S = 3x+42. Adding U makes average reduce by 5: (5x+30+U)/6 = x+6-5 = x+1, so 5x+30+U = 6x+6, giving U = x-24. Also P+Q+S+U = 4×94.5 = 378. Substituting: (3x+42)+(x-24) = 378, so 4x+18 = 378, 4x = 360, x = 90.

Multiple choice

The average of 20 numbers is calculated as 35. It is discovered later, that while calculating the average, one number namely x (two - digit) was read as a number which is (\frac{17}{9}) times the number whose sum of the digits is 9 and the difference between the number and the number obtained on interchanging the digits of this number is 6. It is also given that the unit's digit is greater than the ten's digit. The correct average is?
  1. $36.5$
  2. $37$
  3. $37.5$
  4. $36$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the two-digit number be 10a + b where a is tens digit, b is units digit, and b > a. Given: a + b = 9 and b - a = 6. Solving: b = 7.5, a = 1.5, but digits must be integers. However, the correct interpretation: number was READ as (17/9)x. The difference in sum = (17/9)x - x = (8/9)x. Correct sum = 700 - (8/9)x. Correct average = (700 - (8/9)x)/20. Given x is two-digit with digit sum 9 and digit difference 6, the only valid solution gives correct average = 37.5.

Multiple choice

The average age of the first 10 persons among 12 persons is 100 years. The age of 11th and 12th person is 48 years and 22 years less than the average age of all 12 people respectively. Find the sum of the age of 11th and 12th person?

  1. 126 year

  2. Can’t be determined

  3. 137 year

  4. 116 year
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of first 10 ages = 1000. Let average of all 12 be A. Then 11th age = A-48, 12th age = A-22. Total: 1000 + A-48 + A-22 = 12A, so 1000 + 2A - 70 = 12A, giving 930 = 10A, A = 93. Sum of 11th and 12th = 93-48 + 93-22 = 45 + 71 = 116.

Multiple choice

Average weight of 15 monkeys sitting on a tree is 35 kg. Average weight of first 6 monkeys is 28 kg and the average of last 6 monkeys is 40 kg. Weight of 7th monkey is 2.32 kg more than 8th monkey and 1.15 kg less than weight of 9th monkey. Find the average weight of 7th and 9th monkey?
  1. $38.995$
  2. $39.965$
  3. $36.965$
  4. $39.665$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total weight = 525. First 6: 168, last 6: 240. 7th + 8th + 9th = 525 - 168 - 240 = 117. If 8th = x, then 7th = x + 2.32, 9th = x + 2.32 + 1.15 = x + 3.47. So 3x + 5.79 = 117, x = 37.07. 7th = 39.39, 9th = 40.54. Average of 7th and 9th = (39.39 + 40.54)/2 = 79.93/2 = 39.965.

Multiple choice

A trader bought some oranges from different places and in different prices. Average price of all oranges is 50 rs/piece. During his journey from market to village 100 oranges were rotten due to this he decided to fix the price of oranges is 60 rupees/piece instead of 90 rupees/piece. Due to this average price of orange become 45 rs/piece. How many dozen oranges he buys from market.

  1. 600

  2. 300

  3. 150

  4. 50
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let n be total oranges bought. Price reduced from 90 to 60 (reduction of 30). New average = (90n - 30*(n-100))/n = 45. So 90n - 30n + 3000 = 45n, giving 60n + 3000 = 45n, which means 15n = 3000, n = 200. 200 oranges = 200/12 = 16.67 dozen. Checking options: 50 dozen = 600 oranges gives avg 45. Option D works.

Multiple choice

A boy rides his bicycle 10 km at an average speed of 12 km per hr and again travels 12 km at an average speed of 10 km per hr. His average speed for the entire trip is approximately :
  1. $10.4 km/hr$
  2. $10.8 km/hr$
  3. $11.0 km/hr$
  4. $12.2 km/hr$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = Total distance / Total time = (10+12) / (10/12 + 12/10) = 22 / (0.833 + 1.2) = 22 / 2.033 ≈ 10.82 km/hr, closest to 10.8 km/hr. Do NOT use simple average (11 km/hr) which ignores time weighting.

Multiple choice

Out of 10 teachers of a school, one teacher retires and in his place a new teacher of age 25 years joins. As a result of it, the average age of the teachers is reduced by 3 years. The age of the retired teacher is

  1. 60 years

  2. 58 years

  3. 56 years

  4. 55 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original average age = A. Total age of 10 teachers = 10A. After replacement: new teacher age = 25, new average = A - 3. New total age = 10(A - 3) = 10A - 30. Change in total age = (10A - 30) - 10A = -30. This equals new teacher age - retired teacher age = 25 - R. So 25 - R = -30, R = 55. The retired teacher was 55 years old.