Averages MCQs for UPSC Prelims

45 practice questions on Averages from the Quantitative Aptitude section of the UPSC Prelims syllabus. 45 come with a written explanation and 19 are actual previous year questions. Try the sample set below - the answer stays hidden until you ask for it.

25 Easy 17 Medium 3 Hard 19 from past papers

Sample questions

Q1
Previous year question easy

Two cities A and B are 360 km apart. A car goes from A to B with a speed of 40 km/hr and returns to A with a speed of 60 km/hr. What is the average speed of the car? (a) 45 km/hr (b) 48 km/hr (c) 50 km/hr (d) 55 km/hr

  1. A 45 km/hr
  2. B 48 km/hr
  3. C 50 km/hr
  4. D 55 km/hr
Show answer and explanation

Correct answer: B - 48 km/hr

For equal distances at two speeds, the average speed is the harmonic mean: 2 x s1 x s2 / (s1 + s2) = 2 x 40 x 60 / (40 + 60) = 4800 / 100 = 48 km/hr. (Check: time A to B = 360/40 = 9 hr, time B to A = 360/60 = 6 hr; total distance 720 km in 15 hr = 48 km/hr.)

Q2
Previous year question easy

The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are

  1. A 39
  2. B 39.7
  3. C 40
  4. D 40.3
Show answer and explanation

Correct answer: B - 39.7

The reported total = 100 * 40 = 4000. One student's mark was read as 83 instead of the actual 53, so the total was overstated by 83 - 53 = 30. Corrected total = 4000 - 30 = 3970. Corrected mean = 3970 / 100 = 39.7. Answer (b) 39.7.

Q3
Previous year question medium

Consider a set of 11 numbers: Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers >= -5. Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers. Which one of the following is correct?

  1. A Value-I < Value-II
  2. B Value-II < Value-I
  3. C Value-I = Value-II
  4. D Cannot be determined due to insufficient data
Show answer and explanation

Correct answer: C - Value-I = Value-II

Value-I: the 11 numbers are consecutive integers, each at least -5. The average of 11 consecutive integers is the middle (6th) term, so to minimize it we start as low as allowed: -5, -4, ..., 5, whose average is 0. Any higher starting point raises the average, so the minimum average is 0. Value-II: the 11 numbers are consecutive non-negative integers. Starting at 0 gives 0, 1, ..., 10, whose product is 0 because of the factor 0. Starting at 1 or more gives a large positive product. So the minimum product is 0. Both values equal 0, so Value-I = Value-II. The official UPSC key confirms option (c).

Q4
Previous year question easy

The average score of a batsman after his 50th innings was 46.4. After 60th innings, his average score increases by 2.6. What was his average score in the last ten innings?

  1. A 122
  2. B 91
  3. C 62
  4. D 49
Show answer and explanation

Correct answer: C - 62

Total runs after 50 innings = 50 x 46.4 = 2320. New average after 60 innings = 46.4 + 2.6 = 49, so total runs after 60 innings = 60 x 49 = 2940. Runs scored in the last 10 innings = 2940 - 2320 = 620. Average over those 10 innings = 620 / 10 = 62. Option 49 is the overall average not the last-ten average; 91 and 122 are arithmetic errors.

Q5
Previous year question medium

The average weight of A, B, C is 40 kg, the average weight of B, D, E is 42 kg and the weight of F is equal to that of B. What is the average weight of A, B, C, D, E and F?

  1. A 40.5 kg
  2. B 40.8 kg
  3. C 41 kg
  4. D Cannot be determined as data is inadequate
Show answer and explanation

Correct answer: C - 41 kg

From the averages: A + B + C = 3 x 40 = 120 and B + D + E = 3 x 42 = 126. The required total is A + B + C + D + E + F = (A + B + C) + (B + D + E) - B + F. Since F = B, the -B and +F cancel, leaving 120 + 126 = 246. Average = 246/6 = 41 kg, option (c). The equality F = B is exactly what makes the problem solvable, so option (d), data inadequate, is wrong; options (a) and (b) result from averaging 40 and 42 incorrectly without handling the shared B.

Q6
Previous year question easy

The average monthly income of a person in a certain family of 5 is Rs. 10,000. What will be the average monthly income of a person in the same family if the income of one person increased by Rs. 1,20,000 per year?

  1. A Rs. 12,000
  2. B Rs. 16,000
  3. C Rs. 20,000
  4. D Rs. 34,000
Show answer and explanation

Correct answer: A - Rs. 12,000

Current total monthly income of the family = 5 x 10,000 = Rs. 50,000. One person's income rises by Rs. 1,20,000 per year, which is 1,20,000 / 12 = Rs. 10,000 per month. New total monthly income = 50,000 + 10,000 = Rs. 60,000. New average per person = 60,000 / 5 = Rs. 12,000. The trap answers 16,000 and 20,000 come from adding the yearly figure without converting to monthly. Hence Rs. 12,000.

Q7
Previous year question medium

There are thirteen 2-digit consecutive odd numbers. If 39 is the mean of the first five such numbers, then what is the mean of all the thirteen numbers?

  1. A 47
  2. B 49
  3. C 51
  4. D 45
Show answer and explanation

Correct answer: A - 47

For consecutive odd numbers the mean of any set equals its middle term. The first five numbers have mean 39, so the 3rd number is 39 and the five numbers are 35, 37, 39, 41, 43, making the first number 35. The thirteen consecutive odd numbers are 35, 37, ... up to 35 + 2 x 12 = 59. The mean of all thirteen is the 7th (middle) number = 35 + 2 x 6 = 47. Hence (a).

Q8
Previous year question medium

There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B. Consider the following statements: 1. The average score of Class-B will definitely decrease. 2. The average score of Class-A will definitely increase. Which of the above statements is/are correct?

  1. A 1 only
  2. B 2 only
  3. C Both 1 and 2
  4. D Neither 1 nor 2
Show answer and explanation

Correct answer: A - 1 only

Every student in Class-A scores between 17 and 21, while every student in Class-B scores between 22 and 30. Any four students shifted from A to B therefore score below Class-B's current minimum of 22, so Class-B's average must fall - statement 1 is correct. For Class-A, the effect depends on which students leave: if the four shifted students scored near 17 (below A's average) the remaining average rises, but if they scored near 21 (above A's average) it falls. Since both are possible, statement 2 is not definite. Hence (a) 1 only. Options (b) and (c) wrongly treat statement 2 as certain, and (d) wrongly rejects statement 1.

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More Quantitative Aptitude topics

Number System 188 Permutation, Combination & Probability 94 Percentage 85 Geometry & Mensuration 69 Time, Speed & Distance 66 Algebra 66 Basic Numeracy & Word Problems 66 Ratio & Proportion 60 Clocks & Calendars 56 Sequences & Series 56 Mixtures & Alligation 52 Time & Work 51 Simple & Compound Interest 43 Profit, Loss & Discount 39 Ages 33