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

The system $N_2O_4 \rightleftharpoons 2 NO_2$ maintained in a closed vessel at $60^oC$ & pressure of $5$ atm has an average (i.e. observed) molecular weight of $69$, calculate $K_p$. At what pressure at the same temperature would the observed molecular weight be $(230/3)$?
  1. $K_p = 1.25 atm , P = 15 atm$
  2. $K_p = 2.5 atm , P = 15 atm$
  3. $K_p = 5 atm , P = 30 atm$

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

The average molecular weight M_avg is related to the degree of dissociation alpha by M_avg = M_theoretical / (1 + alpha). For N2O4, M_theoretical = 92. At 5 atm, 69 = 92 / (1 + alpha) implies alpha = 1/3. Kp = (4 * alpha^2 * P) / (1 - alpha^2) = (4 * (1/9) * 5) / (8/9) = 2.5. For the second case, M_avg = 230/3 = 76.67, so 76.67 = 92 / (1 + alpha), giving alpha = 0.2. Using Kp = 2.5 = (4 * 0.2^2 * P) / (1 - 0.2^2), we get P = 15 atm.

Multiple choice

$600$ persons took a dip in a rectangular tank which is $60 m$ long and $40 m$ broad. What is the rise in the level of water in the tank, if the average displacement of water by a person is $0.04\, m^{3}$?
  1. $4 cm$
  2. $3 cm$
  3. $2 cm$
  4. $1 cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total displacement = 600 * 0.04 = 24 m^3. The volume of water displaced equals the area of the tank base times the rise in height: 60 * 40 * h = 24. Thus, h = 24 / 2400 = 0.01 m, which is 1 cm.

Multiple choice

The average age of a group of eight is same as it was 3 years ago when a young member is substituted for an old member the incoming member is younger to the outgoing member by
  1. $11\ years$
  2. $24\ years$
  3. $28\ years$
  4. $16\ years$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Over 3 years, the total age of the 8-member group would normally increase by 8 * 3 = 24 years. Since the average age remains the same after substituting the old member with the young member, the total sum of ages must also remain the same as it was 3 years ago. This means the new member's age must be exactly 24 years less than the outgoing member's current age.

Multiple choice

An average daily wages of $10$ workers in a factory '$A$' is Rs. $30$ and an average daily wages of $20$ workers in a factory '$B$' is Rs. $15$. Find the average daily wages of all workers of both the factories.
  1. $20$
  2. $40$
  3. $10$
  4. $15$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total wages for factory A is 10 * 30 = 300, and for factory B is 20 * 15 = 300. The combined average is the total wages divided by the total number of workers: (300 + 300) / (10 + 20) = 600 / 30 = 20.

Multiple choice

Assume that there are 100 families in a country, the average per capita income of these families is Rs 10,000 and the average per capita income of 50 of these families is Rs 5000. The average per capita income of the remaining families is _____.

  1. Rs 5,000

  2. Rs 10,000

  3. Rs 15,000

  4. Rs 20,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total income is 100 * 10,000 = 1,000,000. The income of 50 families is 50 * 5,000 = 250,000. The remaining 50 families have a total income of 1,000,000 - 250,000 = 750,000, so their average is 750,000 / 50 = 15,000.