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

In a company, the average salary of the boy is Rs. 50,000. The average salary of all the employees is Rs. 48,000. There are 80 boys in the company and the average salary of the girl is Rs. 40,000. What is the number of girls working in the company?

  1. 12

  2. 15

  3. 20

  4. 24
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let G be the number of girls. Total employees = 80 + G. Total salary = 50000 * 80 + 40000 * G. Average salary = (4000000 + 40000G) / (80 + G) = 48000. Solving: 4000000 + 40000G = 3840000 + 48000G. 160000 = 8000G, so G = 20.

Multiple choice

There are 5 packages. The weight of 1st package is 500 kg and the weight of the 2nd package is 50% higher than the weight of 3rd package whose weight is 45% higher than the 1st package weight. The fourth package at 360 kgs is 60% lighter than the fifth package. Find the average weight of all the five packages.

  1. 714.5 kgs

  2. 728.3 kgs

  3. 725.9 kgs

  4. 716.6 kgs

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

P1 = 500. P3 = 500 * 1.45 = 725. P2 = 725 * 1.5 = 1087.5. P4 = 360. P5 = 360 / (1 - 0.6) = 360 / 0.4 = 900. Average = (500 + 1087.5 + 725 + 360 + 900) / 5 = 3572.5 / 5 = 714.5.

Multiple choice

There are 100 students in three departments [X, Y and Z] of a college. Average marks of all the student is 82.7. Average marks of X and Z is 83. Average marks of Y are 82, then find number of students in Y?

  1. 51

  2. 78

  3. 47

  4. 30

  5. 39
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let nX, nY, nZ be students in each. nX+nY+nZ = 100. Total marks = 82.7 * 100 = 8270. (nX+nZ)*83 + nY*82 = 8270. Since nX+nZ = 100 - nY, we have (100-nY)*83 + 82nY = 8270. 8300 - 83nY + 82nY = 8270. nY = 30.

Multiple choice

James owns a garment shop. He sold a total of 4 dresses at an average price of \$8. The next day, he again sold 4 dresses, but this time with an average price of \$10. On the third day, he sold 2 dresses after increasing the price by 10% and then 2 dresses after increasing the price by 20%. The dress before the increase of 10% had the same price as the average price of each dress on the first day, and the dress before the increase of 20% had the same price as the average price of each dress on the second day. What was the average price of all the dresses he sold?
  1. $8.55
  2. $9.12
  3. $9.47
  4. $9.98
  5. $10.22
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Jamie has 14 bottles, each of a different height, in inches. If he adds the heights of two more bottles having the same height, then their average height increases by 1 inch. What is the height of each bottle he added so that the average height after including them is 15 inches?

  1. 14 inches

  2. 20 inches

  3. 22 inches

  4. 32 inches

  5. 44 inches
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let S be the sum of the 14 original heights. The average is S/14. After adding two bottles of height x, the new sum is S + 2x and the new average is (S + 2x)/16 = 15, so S + 2x = 240. We are given that (S + 2x)/16 = S/14 + 1. Substituting S = 240 - 2x into this equation gives (240)/16 = (240 - 2x)/14 + 1, which simplifies to 15 = (120 - x)/7 + 1. Solving for x gives 14 = (120 - x)/7, so 98 = 120 - x, resulting in x = 22.

Multiple choice

Phoebe's factory manufactures toys for small kids. She has compiled data on the number of toys manufactured by her factory workers over the past seven days: 184, 122, 167, 120, 132, 209, 109. If she added the number of toys manufactured on the 8th day, the average for the seven days would increase by 2. What is the difference between the increased average and the number of toys manufactured on the 8th day?

  1. 14

  2. 13

  3. 11

  4. 9

  5. 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let S be the sum of 7 days. Average = S/7. New average = (S+x)/8 = S/7 + 2. S/8 + x/8 = S/7 + 2. x/8 = S/56 + 2. The difference between new average and x is (S+x)/8 - x = (S+x-8x)/8 = (S-7x)/8. This simplifies to 14.

Multiple choice

Consider an arithmetic progression with n terms. If the common difference is increased by 1, then nth term increases by 19. If the 5th term of the progression is 28 and the average of the first and last terms is 61, then the 10th term of the progression is:

  1. 54

  2. 56

  3. 58

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

Let terms be a, a+d, ..., a+(n-1)d. n-th term = a+(n-1)d. If d increases by 1, n-th term = a+(n-1)(d+1) = a+(n-1)d + (n-1). Given increase is 19, so n-1 = 19 => n = 20. 5th term = a+4d = 28. Average of first and last = (a + a+19d)/2 = a+9.5d = 61. System: a+4d=28, a+9.5d=61. Subtract: 5.5d = 33 => d = 6. Then a = 28 - 24 = 4. 10th term = a+9d = 4 + 9(6) = 4 + 54 = 58.