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 average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is

  1. 1 : 2

  2. 3 : 1

  3. 1 : 4

  4. 4 : 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let N1 be original students, N2 be new students, A1 be original average, A2 = A1 + 3. New average = (N1*A1 + N2*(A1+3)) / (N1+N2) = A1 + 0.6. Solving this: 3*N2 = 0.6*(N1+N2) => 2.4*N2 = 0.6*N1 => N1/N2 = 4/1.

Multiple choice

In St. John's Primary school, there are two sections, A and B, in class I each consisting of equal number of students. The average weight of the students in section A and section B are 44 kg and 50 kg, respectively. If one-fifth of the students in section B are moved to section A, the average weight of the students in section A increases by 1 kg. Which of the following is true regarding the average weight of the students in section B after the movement of students to section A?

  1. Decreases

  2. Remains unchanged

  3. Increases

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the number of students in each section. Total weight A = 44n, B = 50n. Moving 1/5n students (average 50) to A: New total weight A = 44n + 0.2n * 50 = 54n. New count A = 1.2n. New average A = 54n / 1.2n = 45. This matches the increase of 1 kg. For B, removing 1/5n students with average weight 50 from a group with average weight 50 leaves the average unchanged.

Multiple choice

In a bookstore, the average price of books sold increased by Rs. 10 when a new collection of books was added. The average price of the new collection of books is Rs. 80 more than half the average price of the original books. If the ratio of the number of original books to the number of books from new collection is 3 : 2, what is the average price of the new collection of books?

  1. 55

  2. 80

  3. 135

  4. 155

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

Let original average = x. Original books = 3k, new books = 2k. Total books = 5k. New average = x + 10. New collection average = 0.5x + 80. Equation: (3k*x + 2k*(0.5x + 80)) / 5k = x + 10. (3x + x + 160) / 5 = x + 10. 4x + 160 = 5x + 50. x = 110. New collection average = 0.5(110) + 80 = 55 + 80 = 135.

Multiple choice

There are three persons A, B and C in a room. If a person D joins the room, the average weight of the persons in the room reduces by x kg. Instead of D, if person E joins the room, the average weight of the persons in the room increases by 2x kg. If the weight of E is 12 kg more than that of D, then the value of x is

  1. 1.5

  2. 2

  3. 0.5

  4. 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let S be sum of weights of A, B, C. (S+D)/4 = S/3 - x. (S+E)/4 = S/3 + 2x. Subtracting: (E-D)/4 = 3x. Given E-D = 12, so 12/4 = 3x. 3 = 3x, x = 1.

Multiple choice

There are two Sections, namely, C and D of a Class, consisting of 30 and 50 students respectively. If the average weight of students of Section C is 45 kg and that of Section D is 50 kg, then find the average weight of students of both the sections overall?

  1. 48.125 kg

  2. 49.250 kg

  3. 40.120 kg

  4. 41.105 kg

  5. 43.115 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total weight = (30 * 45) + (50 * 50) = 1350 + 2500 = 3850. Total students = 80. Average = 3850 / 80 = 48.125 kg.

Multiple choice

In an examination, the average marks of all students was 72. After correcting mistakes, the average marks of 40 students decreased from 80 to 60, while the marks of the remaining students remained unchanged. As a result, the overall average of all students became 70. Find the total number of students.

  1. 450

  2. 410

  3. 428

  4. 400

  5. 475
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let N be the total students. Initial sum = 72N. New sum = 72N - 40(80-60) = 72N - 800. New average = (72N - 800)/N = 70. 72N - 800 = 70N -> 2N = 800 -> N = 400.

Multiple choice

Natasha wants to pursue her B. Tech from ADC University, India, but not able to afford it, she has to take an education loan. The loan agreement guaranteed to pay 80% of all her expenses, this way she only had to bear the remaining costs. She had to pay the rent for her new apartment was Rs. 550 per month. She then paid her tuition for the current semester worth Rs. 25000. On an average she spent Rs. 340 on utilities and groceries per month. Given that, Natasha's course lasted a total of two years (comprising of 2 semesters per year) and the bank gave 80% of the total expenses of two years at the beginning of her course. How much did the bank have to pay in total for two years on behalf of Natasha?

  1. Rs. 90308

  2. Rs. 85428

  3. Rs. 97088

  4. Rs. 90288

  5. Rs. 92286
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Monthly expenses: 550 (rent) + 340 (utilities) = 890. Semester expenses: 890 * 6 = 5340 + 25000 = 30340. Total for 4 semesters (2 years): 30340 * 4 = 121360. Bank pays 80%: 0.8 * 121360 = 97088.

Multiple choice

In a wildlife research centre, the average weight of recorded elephant groups increases by 1.6 quintals when a new group of young elephants is added to the data. If the average weight of the young elephant group is 4 quintals more than that of the average weight of the older elephant groups, what is the ratio of the number of older elephant groups to the number of young elephant groups?

  1. 2 : 5

  2. 3 : 2

  3. 3 : 4

  4. 5 : 3

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

Let N1, A1 be the number and average of older groups, and N2, A2 be for the new group. (N1*A1 + N2*A2) / (N1 + N2) = A1 + 1.6. Given A2 = A1 + 4. Substituting: N1*A1 + N2*(A1 + 4) = (N1 + N2)(A1 + 1.6). N1*A1 + N2*A1 + 4*N2 = N1*A1 + 1.6*N1 + N2*A1 + 1.6*N2. 2.4*N2 = 1.6*N1. N1/N2 = 2.4/1.6 = 3/2.

Multiple choice

The question below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Question: In a family there are 5 members, Nidhi, Vidhi, Nitya, Ajay and Anil. Find the present age of Anil. Statements:I. The average age of five family members is 36 years.II. The total age of Nidhi, Vidhi and Anil is 75 years.III. The present age of Anil is 12 years more than the age of Ajay.

  1. Data in I alone is sufficient

  2. Data in II and III is sufficient

  3. Data in I and II or II and III is sufficient

  4. Data in all the statements I, II and III is not sufficient

  5. Data in all statements together is necessary
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives the sum of 5 ages (36*5 = 180). Statement II gives the sum of 3 ages (75). Statement III relates Anil and Ajay. Even with all three, we have: N+V+Nitya+Ajay+Anil = 180, N+V+Anil = 75, Anil = Ajay+12. Substituting gives Nitya+Ajay+Ajay+12 = 105, which is not enough to isolate Anil's age.