Mixture & Alligation PYQs for UPSC (2011-2024) | Solved Questions & PDF Download

Master Mixture & Alligation for UPSC with solved Previous Year Questions (PYQs) from 2011 to 2024. This page provides detailed solutions, practice questions, and a free downloadable PDF to help you ace your UPSC preparation.

Why Mixture & Alligation Matters in UPSC?

Mixture and Alligation is a crucial topic in the UPSC CSAT (Civil Services Aptitude Test). It tests your ability to:

➡️ Solve ratio-based problems.
➡️ Calculate proportions and averages.
➡️ Understand weighted averages and mixture problems.

This page breaks down the concepts and provides year-wise solved questions to help you master this topic.

Key Concepts in Mixture & Alligation

Before diving into the questions, let’s quickly revise the key concepts:

1. Mixture

➡️ A mixture is formed by combining two or more ingredients.
➡️ Example: Mixing water and milk to form a solution.

2. Alligation

➡️ Alligation is a method to find the ratio in which two or more ingredients are mixed to produce a mixture of a desired concentration.
➡️ Formula:

Quantity of Cheaper Ingredient:Quantity of Dearer Ingredient=(D−M):(M−C)Quantity of Cheaper Ingredient:Quantity of Dearer Ingredient=(D−M):(M−C)

Where:

➡️ CC = Cost of cheaper ingredient
➡️ DD = Cost of dearer ingredient
➡️ MM = Mean cost (desired concentration)

Year-Wise Mixture & Alligation PYQs (2011-2024)

Q1. Two glasses of equal volume are respectively half and three-fourths filled with milk. They are then filled to the brim by adding water. Their contents are then poured into another vessel. What will be the ratio of milk to water in this vessel?

[CSAT 2012]

(a) 1:3

(b) 2:3

(d) 5:3

Solution:

Given that,

Two glasses of equal volume are respectively half and three-fourths filled with milk.

They are then filled to the brim by adding water.

Their contents are then poured into another vessel.

Now,

Milk in first glass = 1/2

Milk in second glass = 3/4

Water in first glass = 1/2

Water in second glass = 1 - 3/4 = 1/4

Thus the ratio = [(1/2) + (3/4)]/[(1/2) + (1/4)] = (5/4)/(3/4) = 5 : 3

Hence option (d) is correct

Q2. Two equal glasses of same type are respectively 1/3 & 1/4 full of milk. They are then filled up with water and the contents are mixed in a pot. What is the ratio of milk and water in the pot? [CSAT 2015]

(a) 7:17

(b) 1:3

(d) 11:23

Solution:

Given that,

Two equal glasses of same type are respectively & full of milk.

They are then filled up with water and the contents are mixed in a pot.

Now,

The total milk in both the glasses = 1/3 + 1/4 = 7/12

Water added in first glass = 1 - 1/3 = 2/3

Water added in second glass = 1 - 1/4 = 3/4

Total water in both the glasses = 2/3 + 3/4 = 17/12

Required ratio = (7/12)/(17/12) = 7/17

Hence option (a) is correct

Q3. 30 g of sugar was mixed in 180 ml water in a vessel A, 40 g of sugar was mixed in 280 ml of water in vessel B and 20 g of sugar was mixed in 100 ml of water in vessel C. The solution in vessel B is. [CSAT 2016]

(a) Sweeter than that in C.

(b) Sweeter than that in A.

(d) Less sweet than that in C.

Solution:

Given that,

30 g of sugar was mixed in 180 ml water in a vessel A

40 g of sugar was mixed in 280 ml of water in vessel B

20 g of sugar was mixed in 100 ml of water in vessel C.

Now,

Calculating the solution of sugar

Vessel A = 30/180 = 1/6 gm/ml

Vessel B = 40/280 = 1/7 gm/ml

Vessel C = 20/100 = 1/5 gm/ml

The more concentration of sugar means more sweetness of solution thus Vessel C > Vessel A > Vessel B

Thus solution in vessel B is less sweet than Vessel C

Hence option (d) is correct

Q4. The monthly average salary paid to all the employees of a company was Rs. 5000. The monthly average salary paid to male and female employees was Rs. 5200 and Rs. 4200 respectively. Then the percentage of males employed in the company is [CSAT 2016]

(a) 75%

(b) 80%

(d) 90%

Solution:

Given that,

The monthly average salary = Rs 5000

The monthly average salary paid to male and female employees = Rs. 5200 and Rs. 4200

Now,

Considering number of employee = 100

Total salary = 100 x 5000 = Rs. 5 x 10⁵ or 5 lakhs

Let the number of males be (M)

Number of females = 100 - M

5 x 10⁵ = 5200 x M + 4200 x (100 - M)

5 x 10⁵ = 1000M + 4.2 x 10⁵

80000 = 1000M

M = 80

Thus females = 100 - 80 = 20

% of male employee = 80%

Hence option (b) is correct

Q5. There is a milk sample with 50% water in it. If of this milk is added to equal amount of pure milk, then water in the new mixture will fall down to [CSAT 2017]

(a) 25%

(b) 30%

(d) 40%

Solution:

Given that,

There is a milk sample with 50% water in it

Now,

Let the milk sample be M litres

If rd of this milk is added to equal amount of pure milk

So, new pure milk = M/3 litres

Added milk sample = M/3 litres

Total milk = 2M/3

From the added sample 1/2 is water = M/6

So, % of water in new mixture of milk = [(M/6)/(2M/3)] x 100

(3/12) x 100 = 25%

Hence option (a) is correct

Q6. A vessel full of water weighs 40 kg. If it is one- third filled, its weight becomes 20 kg. What is the weight of the empty vessel? [CSAT 2020]

(a) 10 kg

(b) 15 kg

(d) 25 kg

Solution:

Given that,

A vessel full of water weighs 40 kg.

If it is one- third filled, its weight becomes 20 kg.

Now,

From the given option

Let's take option (a) where the weight of empty vessel = 10 kg

Weight of water = 40 - 10 = 30kg

If water is 1/3rd filled weight becomes = 30/3 = 10 kg

So weight of vessel and water = 10 + 10 = 20

So weight of empty Vessel is 10 kg

Hence option (a) is correct

Alternate Solution,

Let, X = weight of vessel and Y = weight of water

By Equation as X + Y = 40 kg

X + Y/3 = 20 kg

Q7. Consider the following data:

	Average marks in English	Average marks in Hindi
Girls	9	8
Boys	8	7
Overall Average marks	8.8	X

What is the value of x in the above table? [CSAT 2020]

(a) 7.8

(b) 7.6

(d) 7.2

Solution:

Given that,

To find Hindi overall average scores
Let the class consists of y boys and x girls.

Equations formed using above data are:
The sum of the English scores for boys and girls = 9x + 8y

The average score for all students is 8.8.

Therefore,

(9x + 8y)/(x+y) = 8.8.......(i)

Thus x = 4y......(ii)
For both boys and girls together, the total score in Hindi = (8x + 7y)

Overall average marks in Hindi = (8x + 7y)/(x + y).......(iii)
By substituting the value for x from equation (ii) in (iii)

(8(4y) + 7(y))/(4y+y) = (39y)/(5y) = 7.8.

Thus, 7.8 is the overall average score in Hindi.

Hence option (a) is correct

Q8. A 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? [CSAT 2020]

(a) 4:1

(b) 5:1

(d) 17:8

Solution:

Given that,

A 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.

Now,

As, 4 litres of liquid A is taken out of it and replaced by same quantity of liquid B.

Quantity of liquid A = 16 L, Quantity of liquid B = 4 L

Again 4 litres of the mixture is taken out and replaced by same quantity of liquid B.

Thus,

A : B = {16 - (16/20) x 4} : {4 - [(4/20) x 4] + 4}

Therefore by solving the equation

A : B = 16 : 9

Hence option (c) is correct

Alternate Solution

Using short trick:

The ratio of the original liquid's quantity to the total amount of liquid after n operations is determined if B units of another liquid are substituted for A units of the original liquid n times. = ((A - B) / A)ⁿ.

[(20 - 4)/20]² = (16/20)² = (4/5)² = 16/25

Total quantity = 25 litres

Liquid A = 16 litres

Liquid B = 25 - 16 = 9

Ratio = 16 : 9

Hence option (c) is correct

Q9. There 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? [CSAT 2022]

(a) m = n

(b) m > n

(d) Cannot be determined due to insufficient data.

Solution:

Given that,

There are two containers X and Y.

X contains 100 ml of milk

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

Now,

Total amount of milk left in X after transferring = 100 - 20 = 80ml

Total amount of milk in Y = 100 + 20 = 120 ml

Ratio of milk and water in Y = 20 : 100 = 1 : 5 or total 1/6

Mixture transferred from Y (milk) = 20/6 and water = (20/6) x 5 = 100/6

Left mixture in Y = 20 - (20/6) = 100/6 (milk) and 100 - (100/6) = 500/6 (water) = n

New mixture in X Milk = 80 + (20/6) = 500/6 = m and water = 100/6

Thus m = n

Hence option (a) is correct

Q10. What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey? [CSAT 2024]

(a) 20%

(b) 10%

(d) 4%

Solution:

Given that,

Gain = 20%

Now,

Let the honey be 100 ml and Cost = Rs.1/ml

Thus Cost price = Rs.100

For 20% gain the S.P must be Rs. 120

Difference = Rs. 120 - Rs. 100 = Rs. 20

Thus 20 ml of water must be added

Therefore,

% addition of water in honey = (20/100) x 100 = 20% addition

Hence option (a) is correct

ANSWER KEY

1. D

2. A

3. D

4. B

5. A

6. A

7. A

8. C

9. A

10. A

Download Mixture & Alligation PYQs PDF

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FAQs on Mixture & Alligation for UPSC

1. Is Mixture & Alligation important for UPSC?

➡️ Yes, Mixture & Alligation is a crucial topic for the UPSC CSAT paper. It tests your ability to solve ratio-based problems and calculate proportions.

2. How to prepare for Mixture & Alligation in UPSC?

➡️ Understand basic concepts like ratios, proportions, and weighted averages.
➡️ Practice PYQs regularly.
➡️ Use reliable resources like NCERT books and online platforms like iassetu.com.

3. What are the most frequently asked Mixture & Alligation questions in UPSC?

➡️ Ratio-based mixture problems
➡️ Alligation to find the ratio of mixing
➡️ Weighted average problems

Conclusion

Practicing Mixture & Alligation PYQs is essential for cracking the UPSC CSAT paper. This page provides year-wise solved questions, practice problems, and a free PDF download to help you prepare effectively. Bookmark this page and revisit it regularly for updates.

For more UPSC preparation resources, explore iassetu.com. Happy learning!