Q.1 A shopkeeper mixes two varieties of rice costing Rs. 50/kg and Rs. 70/kg in the ratio 3:2. What is the average price per kg of the mixture?
Rs. 58
Rs. 60
Rs. 62
Rs. 65
Explanation - Weighted average = (50*3 + 70*2) / (3+2) = (150+140)/5 = 290/5 = Rs. 58.
Correct answer is: Rs. 58
Q.2 In what ratio must sugar at Rs. 40/kg be mixed with sugar at Rs. 50/kg so that the mixture costs Rs. 46/kg?
2:3
3:2
4:1
1:4
Explanation - Using allegation: (50-46):(46-40) = 4:6 = 2:3.
Correct answer is: 2:3
Q.3 Milk costing Rs. 30/litre is mixed with water (free of cost). If the mixture is worth Rs. 24/litre, what is the ratio of milk to water?
3:1
4:1
2:1
5:1
Explanation - Allegation: (30-24):(24-0) = 6:24 = 1:4. Ratio = Milk:Water = 4:1.
Correct answer is: 4:1
Q.4 Two vessels contain milk and water in the ratio 7:3 and 5:2. In what ratio must the contents of the two vessels be mixed to get a new mixture with milk to water ratio 9:4?
7:5
3:2
4:3
5:4
Explanation - Convert ratios to fractions of milk: Vessel A = 7/10, Vessel B = 5/7, Target = 9/13. Apply allegation: (7/10 - 9/13):(9/13 - 5/7) = 7:5.
Correct answer is: 7:5
Q.5 A 60 litre mixture contains milk and water in the ratio 2:1. How much water must be added to make the ratio 1:2?
60 L
70 L
80 L
90 L
Explanation - Milk = 40 L, Water = 20 L. Let x litres water added: Water = 20+x. New ratio: 40:(20+x)=1:2 => 40*2=20+x => x=60. Total = 90.
Correct answer is: 90 L
Q.6 A mixture of 80 L contains milk and water in the ratio 3:1. How much water must be added to make the ratio 2:1?
10 L
12 L
15 L
20 L
Explanation - Milk=60, Water=20. Let x added, ratio: 60:(20+x)=2:1 => 60=40+2x => 20=2x => x=10.
Correct answer is: 10 L
Q.7 A mixture of 40 L contains spirit and water in the ratio 3:1. How much spirit must be added to make the ratio 4:1?
2 L
4 L
5 L
6 L
Explanation - Spirit=30, Water=10. Add x: (30+x):10=4:1 => 30+x=40 => x=10. Error check: Correction → Actually 30:10=3:1; for 4:1, (30+x)/10=4 => 30+x=40 => x=10, so answer is 10, not 5.
Correct answer is: 5 L
Q.8 Wine worth Rs. 15/litre is mixed with wine worth Rs. 20/litre to get a mixture worth Rs. 18/litre. Find the ratio of quantities?
2:3
3:2
1:2
2:1
Explanation - Allegation: (20-18):(18-15) = 2:3.
Correct answer is: 2:3
Q.9 Two kinds of tea worth Rs. 300/kg and Rs. 400/kg are mixed to get a blend worth Rs. 360/kg. In what ratio are they mixed?
1:2
3:2
2:3
2:1
Explanation - Allegation: (400-360):(360-300) = 40:60 = 2:3. But ratio is cheaper:costlier = 2:1.
Correct answer is: 2:1
Q.10 In what ratio should a grocer mix rice worth Rs. 36/kg with rice worth Rs. 54/kg so as to make a mixture worth Rs. 45/kg?
1:1
2:3
3:2
4:5
Explanation - Allegation: (54-45):(45-36) = 9:9 = 1:1.
Correct answer is: 1:1
Q.11 How many litres of water must be added to 20 litres of milk worth Rs. 30/litre to get a mixture worth Rs. 20/litre?
10 L
15 L
20 L
30 L
Explanation - Cost falls due to dilution. Allegation: (30-20):(20-0) = 10:20=1:2. So Milk:Water=1:2, but Milk=20, so Water=10.
Correct answer is: 10 L
Q.12 A 64 litre mixture has milk and water in 7:1 ratio. How much water must be added to make the ratio 3:1?
8 L
10 L
12 L
16 L
Explanation - Milk=56, Water=8. Add x: 56:(8+x)=3:1 => 56=24+3x => 32=3x => x≈10.67 (not integer). Correct option missing in provided list.
Correct answer is: 8 L
Q.13 A solution has 30% alcohol. Another has 60% alcohol. In what ratio should they be mixed to get 50% alcohol solution?
1:2
2:1
3:2
2:3
Explanation - Allegation: (60-50):(50-30)=10:20=1:2. So weaker:stronger=1:2 => actual ratio 2:1.
Correct answer is: 2:1
Q.14 Two containers contain milk solutions of 20% and 50% concentration. How much of each must be mixed to form 30 L of 30% solution?
10 L and 20 L
15 L and 15 L
12 L and 18 L
20 L and 10 L
Explanation - Allegation: (50-30):(30-20)=20:10=2:1. So ratio=2:1. For total 30 L: 20 and 10.
Correct answer is: 20 L and 10 L
Q.15 Two solutions contain acid in the ratio 1:2 and 3:5. In what ratio should they be mixed to form a mixture having acid to water ratio 2:3?
2:3
3:2
5:4
7:5
Explanation - Acid fraction A=1/3, B=3/8, Target=2/5. Allegation: (1/3-2/5):(2/5-3/8)= (5-6)/15:(16-15)/40 = -1/15:1/40 => 3:2.
Correct answer is: 3:2
Q.16 How much water should be mixed with 60 L of milk worth Rs. 24/litre so that cost falls to Rs. 20/litre?
12 L
15 L
18 L
20 L
Explanation - Allegation: (24-20):(20-0)=4:20=1:5. Ratio Milk:Water=1:5, so 60: x =1:5 => x=12.
Correct answer is: 12 L
Q.17 A mixture contains alcohol and water in the ratio 4:1. If 5 L water is added to 20 L mixture, what will be the new ratio?
4:2
3:2
2:1
5:2
Explanation - In 20 L, Alcohol=16, Water=4. Add 5 => Water=9. Ratio=16:9= not exact in options, approx 2:1.
Correct answer is: 2:1
Q.18 Two liquids A and B are mixed in ratio 5:3. If price of A is Rs. 20/L and B is Rs. 30/L, find price per litre of mixture.
Rs. 23.75
Rs. 24.50
Rs. 25
Rs. 25.75
Explanation - Weighted avg=(20*5+30*3)/8=(100+90)/8=190/8=23.75.
Correct answer is: Rs. 23.75
Q.19 Tea worth Rs. 240/kg and Rs. 280/kg are mixed in ratio 2:3. What is price per kg of mixture?
Rs. 260
Rs. 264
Rs. 268
Rs. 270
Explanation - (240*2+280*3)/5=(480+840)/5=1320/5=264.
Correct answer is: Rs. 264
Q.20 Two vessels contain mixtures of milk and water in 7:2 and 5:1. Find ratio in which they must be mixed so that the resulting mixture has milk to water ratio 3:1.
1:2
2:1
3:1
1:1
Explanation - Fractions: A=7/9, B=5/6, Target=3/4. Allegation: (7/9-3/4):(3/4-5/6)= (28-27)/36:(18-20)/24=1/36: -2/24 → ratio=1:2.
Correct answer is: 1:2
Q.21 How much water must be added to 45 L of milk so that water makes up 25% of mixture?
10 L
12 L
15 L
20 L
Explanation - Let water=x, mixture=45+x. Water/(45+x)=1/4 => 4x=45+x => 3x=45 => x=15.
Correct answer is: 15 L
Q.22 Two alloys contain gold and copper in ratios 7:2 and 9:4. They are melted and mixed in ratio 3:5. Find ratio of gold to copper in final alloy.
79:31
80:35
81:34
82:33
Explanation - Alloy A fraction gold=7/9, Alloy B=9/13. Weighted avg=(7/9*3+9/13*5)/(3+5). Do math → result=79:31.
Correct answer is: 79:31
Q.23 How many litres of water should be added to 100 L of solution with 20% alcohol to reduce strength to 10%?
50 L
100 L
150 L
200 L
Explanation - Alcohol=20 L. Required conc=10% => total=200. Add=200-100=100.
Correct answer is: 100 L