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 class, the average age of boys is 14 years and that of girls is 12 years. The number of girls is 8 more than the number of boys. What is the average age of all students in the class?

  1. 12.5 years

  2. 13 years

  3. 13.5 years

  4. Data inadequate

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

To find the combined average, we need the number of boys and girls. Let boys = b, then girls = b + 8. Total students = 2b + 8. Weighted average = (14b + 12(b+8))/(2b+8) = (26b + 96)/(2b+8) = (13b + 48)/(b+4). This gives different results for different values of b. For b=8: average = (104+96)/16 = 12.5. For b=12: average = (156+96)/20 = 12.6. The answer varies with the number of boys, so data is inadequate.

Multiple choice

The average temperature on Tuesday, Wednesday and Thursday was (37^0)C. The average temperature on Wednesday, Thursday and Friday was (38^0)C. If the temperature on Friday was (39^0)C. Find the temperature on Tuesday.
  1. $\(38^0\)C$
  2. $\(35^0\)C$
  3. $\(36^0\)C$
  4. $\(34^0\)C$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let T, W, Th, F be temperatures on Tuesday, Wednesday, Thursday, Friday. T + W + Th = 3 × 37 = 111. W + Th + F = 3 × 38 = 114. Given F = 39, so W + Th = 114 - 39 = 75. Substituting: T + 75 = 111, so T = 36. Tuesday's temperature was 36°C.

Multiple choice

If average age of P, Q, R and S is 56 years and the total age of P and R is 24 years. Find the average age of Q and R.

  1. 42 years

  2. 21 years

  3. 24 years

  4. Can't be determined

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

The average of P, Q, R, S is 56, so their total is 4 × 56 = 224. P + R = 24, so Q + S = 224 - 24 = 200. But we need the average of Q and R, not Q and S. Since we don't know R individually, we cannot determine Q + R. Option D is correct. The question misdirects by giving P + R but asking for Q + R.

Multiple choice

The average of 13 papers is 50. The average of the first 7 papers is 42 and that of the last 7 papers is 35. What is the marks of the 7th paper?

  1. 33

  2. 104

  3. 113

  4. 54

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

Sum of 13 papers = 13 × 50 = 650. Sum of first 7 = 7 × 42 = 294. Sum of last 7 = 7 × 35 = 245. The 7th paper is counted in both groups, so: 294 + 245 - 7th paper = 650 → 7th paper = 294 + 245 - 650 = -111. This is impossible, so 'None of these' is correct.

Multiple choice

The average weight of 5 men is decreased by 3 kg when one of them weighing 150 kg is replaced by another person. Find the weight of the new person?

  1. 165 kg.

  2. 138 kg.

  3. 135 kg.

  4. 162 kg.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When one person weighing 150 kg is replaced, the average decreases by 3 kg for 5 men, meaning total weight decreases by 5 × 3 = 15 kg. Therefore, the new person weighs 150 - 15 = 135 kg. Option A (165 kg) would increase the average, not decrease it. Option B (138 kg) and D (162 kg) don't match the calculated 15 kg decrease.

Multiple choice

The average of the even numbers from 1 to 30 is.
  1. $15$
  2. $19$
  3. $17$
  4. $16$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Even numbers from 1 to 30 are: 2, 4, 6, ..., 30. There are 15 even numbers. Sum = (n/2)(first + last) = 15/2 × (2+30) = 15 × 16 = 240. Average = Sum/n = 240/15 = 16. Alternatively, average of an arithmetic progression equals (first + last)/2 = (2+30)/2 = 16.

Multiple choice

If the average weight of 5 persons in a group is 60 kg. The average weight increased by 1 kg when a person left the group and a new person joined the group. What is the weight of the new coming person?

  1. 65 kg.

  2. 60 kg.

  3. 55 kg.

  4. Can’t be determined

  5. 50 kg.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial total weight = 5 × 60 = 300 kg. New total weight = 5 × 61 = 305 kg. Let the person who left have weight x and new person have weight y. Then 300 - x + y = 305, so y - x = 5. Without knowing x, we cannot determine y uniquely. The answer is 'Can't be determined'.

Multiple choice

The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75 of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of there two books?

  1. Rs. 5, Rs. 7.50

  2. Rs. 8, Rs. 12

  3. Rs. 10, Rs. 16

  4. Rs. 12, Rs. 14
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total of 10 books = 10 × 12 = Rs. 120. Sum of 8 books = 8 × 11.75 = Rs. 94. So remaining 2 books sum to Rs. 26. Let cheaper be x, then 1.6x + x = 26 → 2.6x = 26 → x = 10, other = 16. Checking: Rs. 10 + Rs. 16 = Rs. 26 ✓ and 16 is 60% more than 10 (1.6 × 10 = 16) ✓

Multiple choice

The average of five numbers is 306.4. Average of first two number is 431 and last two numbers is 214.5. Find the third number.

  1. 239

  2. 241

  3. 243

  4. 245
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the five numbers be a, b, c, d, e. Given: (a+b+c+d+e)/5 = 306.4, so sum = 1532. Also: (a+b)/2 = 431, so a+b = 862. And: (d+e)/2 = 214.5, so d+e = 429. Therefore c = 1532 - 862 - 429 = 241. This checks out: 1532 - 1291 = 241. Option D (243) would leave sum = 1534, which doesn't match.

Multiple choice

Nine persons went to a hotel for taking their meals. Eight of them spent Rs. 12 each over their meals and the ninth spent Rs. 8 more than the average expenditure of all the nine. Total money spent by them was

  1. Rs. 104

  2. Rs. 105

  3. Rs. 116

  4. Rs. 117

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

Let average expenditure of all 9 persons = x. Total expenditure = 9x. Eight persons spent Rs. 12 each = Rs. 96. Ninth person spent x + 8. So 9x = 96 + x + 8 = 104 + x. Therefore 8x = 104, x = 13. Total = 9 × 13 = 117. The ninth person spent 13 + 8 = Rs. 21.

Multiple choice

The average marks of 20 students is 45. The average marks of the first 10 students is 50 and that of the last 9 students is 40. What is the marks of the eleventh student?

  1. 30

  2. 0

  3. 40

  4. 45

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

Total marks of 20 students = 20 × 45 = 900. Sum of first 10 students = 10 × 50 = 500. Sum of last 9 students = 9 × 40 = 360. Marks of eleventh student = Total - (Sum of first 10 + Sum of last 9) = 900 - (500 + 360) = 900 - 860 = 40. Option C matches.

Multiple choice

The average age of the students of a class is 22 years. 12 new students with an average age of 17 years join the class, thereby decreasing the average by 2 years. The original strength of the class was -

  1. 16

  2. 17

  3. 18

  4. 19
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original students = n. Total age = 22n. After 12 students join: new average = 20, new total = (n+12)×20. Also new total = 22n + 12×17 = 22n + 204. So (n+12)×20 = 22n + 204. 20n + 240 = 22n + 204. 2n = 36, n = 18. Set up the equation using weighted averages.