52 practice questions on Mixtures & Alligation from the Quantitative Aptitude section of the UPSC Prelims syllabus.
52 come with a written explanation and 8 are actual previous year questions.
Try the sample set below - the answer stays hidden until you ask for it.
6 Easy28 Medium18 Hard8 from past papers
Sample questions
Q1
Previous year questionmedium
What 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%
Show answer and explanation
Correct answer: A - 20%
Let honey cost Rs. 1 per litre and take 1 litre of honey mixed with w litres of free water. Cost price = Rs. 1. Selling the whole mixture at the cost price of honey gives revenue = (1 + w) x 1. Profit = w on a cost of 1, and we need a 20% gain, so w = 0.20. Water added is 20% of the honey. Hence 20%.
Q2
Previous year questionmedium
There is a milk sample with 50% water in it. If 1/3rd of this milk is added to equal amount of pure milk, then water in the new mixture will fall down to
A25%
B30%
C35%
D40%
Show answer and explanation
Correct answer: A - 25%
Take the sample as 6 units (so the arithmetic stays whole). It is 50% water, so it has 3 units water and 3 units milk. Take 1/3 of this sample = 2 units, which still being half-and-half contains 1 unit water and 1 unit milk. To this we add an equal amount (2 units) of pure milk. New mixture = 2 + 2 = 4 units, of which water = 1 unit. Water percentage = 1/4 = 25%. Hence (a).
Q3
Previous year questioneasy
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?
A1 : 3
B2 : 3
C3 : 2
D5 : 3
Show answer and explanation
Correct answer: D - 5 : 3
Let each glass have volume V. Glass 1 is half milk: milk = V/2, water = V/2. Glass 2 is three-fourths milk: milk = 3V/4, water = V/4. Total milk = V/2 + 3V/4 = 2V/4 + 3V/4 = 5V/4. Total water = V/2 + V/4 = 2V/4 + V/4 = 3V/4. Ratio of milk to water = (5V/4) : (3V/4) = 5 : 3. Hence (d).
Q4
Previous year questionmedium
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?
A4 : 1
B5 : 1
C16 : 9
D17 : 8
Show answer and explanation
Correct answer: C - 16 : 9
Use the replacement formula: remaining A = initial x (1 - (removed/total))^n, with two operations. Remaining A = 20 x (1 - 4/20)^2 = 20 x (16/20)^2 = 20 x (4/5)^2 = 20 x 16/25 = 12.8 litres. Liquid B = 20 - 12.8 = 7.2 litres. Ratio A : B = 12.8 : 7.2 = 128 : 72 = 16 : 9. The other options come from doing a single replacement or arithmetic slips.
Q5
Previous year questionmedium
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?
Am = n
Bm > n
Cm < n
DCannot be determined due to insufficient data
Show answer and explanation
Correct answer: A - m = n
Track the volumes. After moving 20 ml of milk, Y has 20 ml milk + 100 ml water = 120 ml. Returning 20 ml of this uniform mixture sends back 20 x (20/120) = 10/3 ml milk and 20 x (100/120) = 50/3 ml water. X now holds 80 + 10/3 = 250/3 ml milk in 100 ml, so m = 5/6. Y now holds 100 - 50/3 = 250/3 ml water in 100 ml, so n = 5/6. Hence m = n, option (a). This equality is forced: both containers end at 100 ml, so the water that entered X exactly equals the milk left in Y. Options (b) and (c) assume an asymmetry that does not exist, and option (d) is wrong because the data fully determine the answer.
Q6
Previous year questioneasy
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:
Asweeter than that in C
Bsweeter than that in A
Cas sweet as that in C
Dless sweet than that in C
Show answer and explanation
Correct answer: D - less sweet than that in C
Sweetness depends on the sugar-to-water concentration. A = 30/180 = 0.167 g/ml, B = 40/280 = 0.143 g/ml, C = 20/100 = 0.20 g/ml. So C is the sweetest, then A, then B. B (0.143) is less concentrated than C (0.20), so B is less sweet than C. B is also less sweet than A, and it is not equal to C, which eliminates the other options.
Q7
Previous year questioneasy
Two equal glasses of same type are respectively 1/3 and 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?
A7 : 17
B1 : 3
C9 : 21
D11 : 23
Show answer and explanation
Correct answer: A - 7 : 17
Take each glass to hold 12 units (LCM of 3 and 4). First glass: milk = 12/3 = 4, water = 8. Second glass: milk = 12/4 = 3, water = 9. Combined in the pot: milk = 4 + 3 = 7, water = 8 + 9 = 17. So the ratio of milk to water is 7 : 17. Hence option (a).
Q8
Previous year questioneasy
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:
A75%
B80%
C85%
D90%
Show answer and explanation
Correct answer: B - 80%
Let the fraction of males be m. Then 5200m + 4200(1 - m) = 5000. Simplifying: 4200 + 1000m = 5000, so 1000m = 800, giving m = 0.8 = 80%. By alligation, the distance of the mean (5000) from female average (4200) is 800 and from male average (5200) is 200, giving male:female ratio = 800:200 = 4:1, i.e., 80% males.
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