UPSC Prelims PYQ › Quantitative Aptitude › Average, Mixtures & Alligation
Average, Mixtures & Alligation — UPSC CSAT Paper II Quantitative Aptitude previous year questions
20 free solved previous year questions on Average, Mixtures & Alligation, papers from 2017 to 2026, drawn from UPSC CSAT, UPSC CAPF, covering questions of the kind UPSC asks in CSAT Paper II. Every answer key has been checked again against published sources and solved independently, and each explanation is written fresh.
Read all 20 questions with answers
- #1UPSC CSAT 2026The class average x in a test increases by 4 when the score of a student is rectified, whose corrected score is 100 instead of 0. Later, the score of another student was found to have been recorded as 81 in place of 56. If there are no other corrections and the final corrected average is y, then y – x is
- A2
- B3
- C5
- D6
Answer: (B) 3Explanation
Let the class have n students. Fixing a score from 0 to 100 adds 100 to the total.
Average rises by 4, so 100 ÷ n = 4 and n = 25.
The average is now x + 4.
A score recorded as 81 should have been 56. The total falls by 81 – 56 = 25.
Average falls by 25 ÷ 25 = 1.
Final average y = x + 4 – 1 = x + 3.
So y – x = 3, option (b).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #2UPSC CSAT 2026An alloy P contains 20% copper and 80% zinc by weight. Another alloy Q contains 60% copper and 40% zinc by weight. A third alloy R is to be prepared from P and Q so that it contains equal amount of copper and zinc. In what ratio, amounts of P and Q be mixed in order to get R?
- A1 : 3
- B3 : 1
- C2 : 3
- D3 : 2
Answer: (A) 1 : 3Explanation
Let the copper share in alloy R be 50%, as copper and zinc are equal.
P has 20% copper, Q has 60% copper.
By alligation: P : Q = (60 – 50) : (50 – 20) = 10 : 30.
So P : Q = 1 : 3.
Check with 1 kg P and 3 kg Q: copper = 0.2 + 1.8 = 2 kg out of 4 kg, which is 50%.
Answer: option (a).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #3UPSC CSAT 2026There are two chemicals which do not react with each other. A container contains 10 litres of the chemical A. One litre of this chemical is removed from it and one litre of the chemical B is poured. Then one litre of the mixture is removed from the container and one litre of B is poured. If this process of replacing one litre of the mixture by one litre of B is performed once more, then what is the volume of B that is present in the container approximately (in percentage)?
- A25
- B27
- C29
- D31
Answer: (B) 27Explanation
Each time one litre of the mixture is replaced, 9/10 of chemical A is kept.
After 3 replacements, A left = 10 × (0.9)³ = 10 × 0.729 = 7.29 litres.
B present = 10 – 7.29 = 2.71 litres.
As a percentage of 10 litres, that is 27.1%.
Answer: about 27%, option (b).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #4UPSC CSAT 2025The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What is the value of r?
- Ak
- Bk - 1
- Ck + 1
- Dk/2
Answer: (A) kExplanation
p - k = k - q gives p + q = 2k.
Also p + q + r = 3k, so r = 3k - 2k = k.
Answer: option (a).Source: UPSC CSAT 2025 question; answer key checked by independent computation
- #5UPSC CSAT 2024What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey?
- A20%
- B10%
- C5%
- D4%
Answer: (A) 20%Explanation
Let 100 units of honey cost 100. Adding x units of water gives 100 + x units, sold at honey's cost price per unit for 100 + x.
A 20% gain needs 100 + x = 120, so x = 20, i.e. 20% of the honey.
Answer: option (a).Source: UPSC CSAT 2024 question; answer key checked by independent computation
- #6UPSC CSAT 2024Consider the following:Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 womenIf the average weight of the women is 63 kg, then what is the average weight of the boys?
- A40 kg
- B42 kg
- C45 kg
- D63 kg
Answer: (B) 42 kgExplanation
Total weight of 4 women = 4 x 63 = 252 kg.
This equals the total weight of 6 boys.
Average boy = 252/6 = 42 kg. Answer: option (b).Source: UPSC CSAT 2024 question; answer key checked by independent computation
- #7UPSC CSAT 2022There are two containers X and Y. X contains 100 ml of milk and Y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?
- Am = n
- Bm > n
- Cm < n
- Dcannot be determined due to insufficient data
Answer: (A) m = nExplanation
After the first transfer Y has 120 ml: 20 ml milk, 100 ml water. Returning 20 ml takes back 20/6 ml milk and 100/6 ml water.
X then has 80 + 10/3 = 250/3 ml milk in 100 ml. Y keeps 100 - 50/3 = 250/3 ml water in 100 ml.
Both proportions are 250/300, so m = n.
Answer: option (a).Source: UPSC CSAT 2022 question; answer key checked by independent computation
- #8UPSC CSAT 2022The 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?
- A40.5 kg
- B40.8 kg
- C41 kg
- DCannot be determined as data is inadequate
Answer: (C) 41 kgExplanation
A+B+C = 120 and B+D+E = 126.
Since F = B, the sum of all six = (A+B+C) + (D+E+F) = 120 + 126 = 246.
Average = 246/6 = 41 kg.
Answer: option (c).Source: UPSC CSAT 2022 question; answer key checked by independent computation
- #9UPSC CSAT 2021There 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?
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Answer: (A) 1 onlyExplanation
Class-B's average is at least 22, while each shifted student scored at most 21. Adding lower scores must pull B's average down, so statement 1 is true.
Class-A's average lies between 17 and 21. If the four shifted students scored above A's average, A's average falls; so statement 2 is not certain.
Answer: option (a).Source: UPSC CSAT 2021 question; answer key checked by independent computation
- #10UPSC CSAT 2020Consider the following data: | Average marks in English | Average marks in HindiGirls | 9 | 8Boys | 8 | 7Overall average marks | 8.8 | xWhat is the value of x in the above table?
- A7.8
- B7.6
- C7.4
- D7.2
Answer: (A) 7.8Explanation
Let girls : boys = G : B. English: (9G + 8B)/(G+B) = 8.8 gives 0.2G = 0.8B, so G = 4B.
Hindi: x = (8x4 + 7x1)/5 = 39/5 = 7.8.
Answer: option (a).Source: UPSC CSAT 2020 question; answer key checked by independent computation
- #11UPSC CSAT 2020The average age of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher?
- A25 years
- B30 years
- C35 years
- D45 years
Answer: (C) 35 yearsExplanation
Total age = 4 x 20 = 80, so T + 3S = 80. Also T - S = 20.
Subtracting: 4S = 60, S = 15, so T = 35.
Answer: option (c).Source: UPSC CSAT 2020 question; answer key checked by independent computation
- #12UPSC CSAT 2020A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replaced by same quantity of liquid B. Again 4 litres of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?
- A4 : 1
- B5 : 1
- C16 : 9
- D17 : 8
Answer: (C) 16 : 9Explanation
Each replacement keeps (1 - 4/20) = 4/5 of the liquid A.
A left = 20 x 4/5 x 4/5 = 12.8 L, so B = 7.2 L.
Ratio = 12.8 : 7.2 = 16 : 9.
Answer: option (c).Source: UPSC CSAT 2020 question; answer key checked by independent computation
- #13UPSC CSAT 2020The 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?
- A122
- B91
- C62
- D49
Answer: (C) 62Explanation
Runs after 50 innings = 50 x 46.4 = 2320. After 60 innings the average is 49, so runs = 2940.
Runs in last ten = 2940 - 2320 = 620, an average of 62.
Answer: option (c).Source: UPSC CSAT 2020 question; answer key checked by independent computation
- #14UPSC CSAT 2019The 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
- A39
- B39.7
- C40
- D40.3
Answer: (B) 39.7Explanation
Original total = 4000.
The total was overstated by 83 - 53 = 30, so corrected total = 3970.
Corrected mean = 3970/100 = 39.7.
Answer: option (b).Source: UPSC CSAT 2019 question; answer key checked by independent computation
- #15UPSC CSAT 2019Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is
- A13 units
- B15 units
- C16 units
- D30 units
Answer: (D) 30 unitsExplanation
Single-digit odd primes are 3, 5, 7, average 5, so first piece = 5.
Let second = S, third = 5 + S. Then S = 5 + (5 + S)/3, giving S = 10 and third = 15.
Sheet length = 5 + 10 + 15 = 30 units.
Answer: option (d).Source: UPSC CSAT 2019 question; answer key checked by independent computation
- #16UPSC CSAT 2019A family has two children along with their parents. The average of the weights of the children and their mother is 50 kg. The average of the weights of the children and their father is 52 kg. If the weight of the father is 60 kg, then what is the weight of the mother?
- A48 kg
- B50 kg
- C52kg
- D54kg
Answer: (D) 54kgExplanation
Children + father = 3 x 52 = 156, so children together weigh 96 kg.
Children + mother = 3 x 50 = 150.
Mother = 150 - 96 = 54 kg.
Answer: option (d).Source: UPSC CSAT 2019 question; answer key checked by independent computation
- #17UPSC CSAT 2018A lift has the capacity of 18 adults or 30 children. How many children can board the lift with 12 adults?
- A6
- B10
- C12
- D15
Answer: (B) 10Explanation
12 adults use 12/18 = 2/3 of the capacity.
The remaining 1/3 of the capacity holds 30 / 3 = 10 children.
Answer: option (b).Source: UPSC CSAT 2018 question; answer key checked by independent computation
- #18UPSC CSAT 2017Suppose the average weight of 9 persons is 50 kg. The average weight of the first 5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg. Then the weight of the 5th person will be
- A45 kg
- B47.5 kg
- C50 kg
- D52.5 kg
Answer: (C) 50 kgExplanation
Total of 9 = 450 kg; first five = 225 kg; last five = 275 kg.
The 5th person is counted in both groups.
Weight = 225 + 275 - 450 = 50 kg.
Answer: option (c).Source: UPSC CSAT 2017 question; answer key checked by independent computation
- #19UPSC CSAT 2017There 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?
- A47
- B49
- C51
- D45
Answer: (A) 47Explanation
The mean of five consecutive odd numbers is the middle one, so the third number is 39 and the first is 35.
The thirteen numbers run from 35 to 59.
Their mean is the 7th (middle) number, 47.
Answer: option (a).Source: UPSC CSAT 2017 question; answer key checked by independent computation
- #20UPSC CAPF 2018Suppose a, b, c, d and e are five consecutive odd numbers in ascending order. Consider the following statements:1. Their average is (a + 4).2. Their average is (b + 2).3. Their average is (e - 4).Which of the statements given above is/are correct?
- A1 only
- B2 and 3 only
- C1 and 3 only
- D1, 2 and 3
Answer: (D) 1, 2 and 3Explanation
For consecutive odd numbers the average equals the middle number c.
c = a + 4 = b + 2 = e - 4, since the numbers differ by 2.
So all three statements hold.
Answer: option (d).Source: UPSC CAPF 2018 question; answer key checked by independent computation
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