Alligation or Mixture problems
- 1. A jar was full with honey. A person used to draw out 20% of the honey from the jar and replaced it with sugar solution. He has repeated the same process 4 times and thus there was only 512 gm of honey left in the jar, the rest part of the jar was filled with the sugar solution. The initial amount of honey in the jar was:
Options- A. 1.25 kg
- B. 1 kg
- C. 1.5 kg
- D. None of these Also asked in: CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 1.25 kg
Explanation:
Let the initial amount of honey in the jar was k, then
=>
=> k = 1250
Hence initially the honey in the jar = 1.25 kg
- 2. In a 40 litre mixture of alcohol & water, the ratio of alcohol and water is 5 : 3. If 20% of this mixture is taken out and the same amount of water is added then what will be the ratio of alcohol and water in final mixture?
Options- A. 1:1
- B. 2:1
- C. 3:1
- D. 1:2 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 1:1
Explanation:
Quantity of alohol in the mixture = 40 x 5/8 = 25 lit
Quantity of water = 40 - 25 = 15 lit
According to question,
Required ratio =
- 3. The amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol is ?
Options- A. 6 ml
- B. 11 ml
- C. 15 ml
- D. 9 ml Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 6 ml
Explanation:
Let us assume that the lotion has 50% alcohol and 50% water.
ratio = 1:1
As the total solution is 9ml
alcohol = water = 4.5ml
Now if we want the quantity of alcohol = 30%
The quantity of water = 70%
The new ratio = 3:7
Let x ml of water be added
We get,
=> x=6
Hence 6ml of water is added.
- 4. A mixture of 70 litres of Fruit Juice and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12.5% water ?
Options- A. 2 lit
- B. 4 lit
- C. 1 lit
- D. 3 lit Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 2 lit
Explanation:
Quantity of fruit juice in the mixture = 70 - [70 x (10/100) ]= 63 litres.
After adding water, juice would form 87.5% of the mixture.
Hence, if quantity of mixture after adding x liters of water, [(87.5) /100 ]*x = 63 => x = 72
Hence 72 - 70 = 2 litres of water must be added.
- 5. Milk and water are mixed in a vessel A as 4:1 and in vessel B as 3:2. For vessel C, if one takes equal quantities from A and B, find the ratio of milk to water in C.
Options- A. 1:9
- B. 9:1
- C. 3:7
- D. 7:3 Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 7:3
Explanation:
Ratio of Milk and water in a vessel A is 4 : 1
Ratio of Milk and water in a vessel B is 3 : 2
Ratio of only milk in vessel A = 4 : 5
Ratio of only milk in vessel B = 3 : 5
Let 'x' be the quantity of milk in vessel C
Now as equal quantities are taken out from both vessels A & B
=> 4/5 : 3/5
x
3/5-x x - 4/5
=> = (equal quantities)
=> x = 7/10
Therefore, quantity of milk in vessel C = 7
=> Water quantity = 10 - 7 = 3
Hence the ratio of milk & water in vessel 3 is 7 : 3
- 6. The concentration of glucose in three different mixtures (glucose and alcohol) is 12,35 and 45 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. What is the ratio of glucose and alcohol in the new mixture?
Options- A. 3:2
- B. 4:3
- C. 2:3
- D. 3:4 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 3:2
Explanation:
Concentration of glucose are in the ratio =
Quantity of glucose taken from A = 1 liter out of 2
Quantity of glucose taken from B = 3/5 x 3 = 1.5 lit
Quantity of glucose taken from C = 0.8 lit
So, total quantity of glucose taken from A,B and C = 3.6 lit
So, quantity of alcohol = (2 + 3 + 1) - 3.6 = 2.4 lit
Ratio of glucose to alcohol = 3.6/2.4 = 3:2
- 7. One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.
Options- A. 27 %
- B. 26 %
- C. 29 %
- D. 21 % Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO, Network Engineer, Project Manager
Correct Answer: 27 %
Explanation:
Let the percentage of benzene = X
(30 - X)/(X- 25) = 6/4 = 3/2
=> 5X = 135
X = 27
So, required percentage of benzene = 27 %
- 8. Equal quantities of three mixtures of milk and water are mixed in the ratio 1:2, 2:3 and 3:4. The ratio of water and milk in the mixture is ?
Options- A. 193 : 122
- B. 97 : 102
- C. 115 : 201
- D. 147 : 185 Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 193 : 122
Explanation:
Given the three mixtures ratio as (1:2),(2:3),(3:4)
(1+2),(2+3),(3+4)
Total content = 3,5,7
Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105
105/3 = 35 , 105/5 = 21 , 105/7 = 15
Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)
i.e (35,70), (42,63), (45,60)
So overall mixture ratio of milk and water is
35+42+45 : 70+63+60
122:193
But in the question asked the ratio of water to milk = 193 : 122
- 9. The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?
Options- A. 8:3
- B. 6:7
- C. 7:5
- D. 11:7 Also asked in: CAT, Bank Exams, AIEEE, Bank PO
Correct Answer: 7:5
Explanation:
Milk in 1-litre mixture of A = 4/7 litre.
Milk in 1-litre mixture of B = 2/5 litre.
Milk in 1-litre mixture of C = 1/2 litre.
By rule of alligation we have required ratio X:Y
X : Y
4/7 2/5
\ /
(Mean ratio)
(1/2)
/ \
(1/2 ? 2/5) : (4/7 ? 1/2)
1/10 1/1 4
So Required ratio = X : Y = 1/10 : 1/14 = 7:5
- 10. An alloy of copper and bronze weight 50g. It contains 80% Copper. How much copper should be added to the alloy so that percentage of copper is increased to 90%?
Options- A. 45 gm
- B. 50 gm
- C. 55 gm
- D. 60 gm Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 50 gm
Explanation:
Initial quantity of copper = = 40 g
And that of Bronze = 50 - 40 = 10 g
Let 'p' gm of copper is added to the mixture
=> = 40 + p
=> 45 + 0.9p = 40 + p
=> p = 50 g
Hence, 50 gms of copper is added to the mixture, so that the copper is increased to 90%.
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