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

A book distributor sends out standardized packages weighing $1, 1.5$ or $2$ kilograms. If during one week $40$ per cent of the packages weigh $1$ kg, $50$ per cent weigh $1.5$ kg and $10$ per cent weigh $2$ kg, what is the average weight in kilograms of the parcels that week?

  1. 1.10

  2. 1.20

  3. 1.25

  4. 1.35
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The average weight is calculated by the weighted mean: (0.40 * 1) + (0.50 * 1.5) + (0.10 * 2). This equals 0.40 + 0.75 + 0.20 = 1.35 kg.

Multiple choice

In a History examination, the average for the entire class was $80$ marks. If $10$% of the student scored $95$ marks and $20$% scored $90$ marks, what was the average marks of the remaining students of the class?
  1. $65.5$
  2. $72.5$
  3. $75$
  4. $85$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total students be 100. Total marks = 100 * 80 = 8000. 10 students scored 95 (950 marks), 20 students scored 90 (1800 marks). Remaining 70 students scored 8000 - 2750 = 5250. Average = 5250 / 70 = 75.

Multiple choice

Ranjan purchased 120 tables at a price of Rs. 110 per table. He sold 30 tables at a profit of Rs. 12 per table and 75 tables at a profit of Rs. 14 per table. The remaining tables were sold at a loss of Rs. 7 per table. What is the average profit per table?

  1. Rs. 10.04

  2. Rs. 10.875

  3. Rs. 12.80

  4. Rs. 12.875
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total tables = 120. Cost = 120 * 110 = 13200. Profit 1 = 30 * 12 = 360. Profit 2 = 75 * 14 = 1050. Loss = (120 - 30 - 75) * 7 = 15 * 7 = 105. Net profit = 360 + 1050 - 105 = 1305. Average profit = 1305 / 120 = 10.875.

Multiple choice

In an examination , the average marks obtained by students who passed was $x$ $\%$, while the average of those who failed was $y$ $\%$. The average marks of student taking the exam was $z$ $\%$. Find in terms of $x, y$ and $z$ the percentage of students taking the exam who failed ?
  1. $\displaystyle\frac { { \left( z-x \right) }}{{ \left( y-x \right) }}$
  2. $\displaystyle \frac {{ \left( x-z \right) }}{{ \left( y-z \right) }}$
  3. $\displaystyle \frac {{ \left( y-x \right) }}{{ \left( z-y \right) }}$
  4. $\displaystyle \frac {{ \left( y-z \right) }}{{ \left( x-z \right) }}$

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

Let P be the percentage of students who passed and F be the percentage who failed. Then P + F = 100. The total average is z = (x*P + y*F) / 100. Substituting P = 100 - F, we get 100z = x(100 - F) + yF, which simplifies to 100z = 100x - xF + yF. Solving for F gives F = 100 * (z - x) / (y - x). The option A represents this ratio.

Multiple choice

Rakesh consumes an average of $1680$ calories per day.On the day of his finals, Rakesh consumes $12\%$ more calories per day than he usually does. During the last day of finals, he celebrates by consuming an additional $900$ calories. Which of the following represents the total number of calories Rakesh consumes during d days of finals?
  1. $\displaystyle 1.12(1680d+900)$
  2. $\displaystyle 1.12(1680d)+900$
  3. $\displaystyle 1.12(1680+900)d$
  4. $\displaystyle (180+0.12d)+900$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rakesh consumes 1680 calories per day. During d days, he consumes 1.12 * 1680 per day. Total for d days is 1.12 * 1680 * d. He adds 900 on the last day, so the total is 1.12 * 1680 * d + 900.

Multiple choice

The average weight of 120 students in the second year class of college is 56 kg. If the average weight of boys and that of girls in the class are 60 kg and 50 kg respectively, then number of boys and girls in the class are respectively :

  1. 72 , 64

  2. 38 , 64

  3. 72, 48

  4. 62 , 58
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the alligation method: boys average 60, girls 50, overall 56. The difference ratios are (56-50) : (60-56) = 6 : 4 = 3 : 2. Total students 120, so boys = (3/5)*120 = 72 and girls = (2/5)*120 = 48.

Multiple choice

In the first four papers of $100$ marks each, Rishi got $95, 72, 73, 83$ marks respectively. If he wants an average of greater than or equal to $75$ marks and less than $80$ marks, find the range of marks he should score in the fifth paper.
  1. $52 \le x < 77$
  2. $25 < x < 75$
  3. $75 < x < 80$
  4. $73 < x < 100$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of 4 papers = 95+72+73+83 = 323. Let x be the 5th mark. Average = (323+x)/5. 75 <= (323+x)/5 < 80. 375 <= 323+x < 400. 52 <= x < 77.

Multiple choice

One adult and $10$ children are in an elevator. If the adult's weight is $4$ times the average (arithmetic mean) weight of the children, then the adult's weight is what fraction of the total weight of the $11$ people in the elevator?
  1. $\dfrac{2}{7}$
  2. $\dfrac{3}{7}$
  3. $\dfrac{4}{7}$

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A be the adult's weight and C be the average weight of the 10 children. A = 4C. Total weight of children = 10C. Total weight of all 11 people = A + 10C = 4C + 10C = 14C. Adult's fraction = A / (A + 10C) = 4C / 14C = 4/14 = 2/7.