Alligation or Mixture problems
- 1. The diluted wine contains only 8 liters of wine and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing wine. How many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture?
Options- A. 4
- B. 5
- C. 8
- D. None of these Also asked in: CAT, Bank Exams, Bank PO, Bank Clerk
Correct Answer: 5
Explanation:
Wine Water
8L 32L
1 : 4
20 % 80% (original ratio)
30 % 70% (required ratio)
In ths case, the percentage of water being reduced when the mixture is being replaced with wine.
so the ratio of left quantity to the initial quantity is 7:8
Therefore ,
=> K = 5 Lit
- 2. The ratio of water and alcohol in two different containers is 2:3 and 4:5. In what ratio we are required to mix the mixtures of two containers in order to get the new mixture in which the ratio of alcohol and water be 7:5?
Options- A. 7:3
- B. 5:3
- C. 8:5
- D. 2:7 Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 5:3
Explanation:
2 : 3 4 : 5 5 : 7
= 72/180
= 80/180
= 75/180
=> 5 : 3
Therefore, the ratio is 5: 3
- 3. In a pot, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk, the pot would be full and ratio of milk and water would become 6 : 5. Find the capacity of the pot?
Options- A. 11 lit
- B. 22 lit
- C. 33 lit
- D. 44 lit Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 22 lit
Explanation:
Let the capacity of the pot be 'P' litres.
Quantity of milk in the mixture before adding milk = 4/9 (P - 8)
After adding milk, quantity of milk in the mixture = 6/11 P.
6P/11 - 8 = 4/9(P - 8)
10P = 792 - 352 => P = 44.
The capacity of the pot is 44 liters.
- 4. Ratio of water and milk in a container is 2 : 3. If 40 liter mixture removed from the container and same quantity of milk is added to it then the ratio of water to milk becomes 1 : 4. Find the initial quantity of mixture?
Options- A. 75 lit
- B. 80 lit
- C. 85 lit
- D. 90 lit Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 80 lit
Explanation:
From the given data,
let the initial quantity of the mixture = 5x
Then,
Then the initial quantity of the mixture = 5x = 5 x 16 = 80 lit.
- 5. From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus, in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the container was:
Options- A. 75 litres
- B. 100 litres
- C. 150 litres
- D. 120 litres Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 120 litres
Explanation:
It means (since 343 + 169 = 512)
Thus,
Thus the initial amount of wine was 120 liters.
- 6. A tin a mixture of two liquids A and B in the proportion 4 : 1. If 45 litres of the mixture is replaced by 45 litres of liquid B, then the ratio of the two liquids becomes 2 : 5. How much of the liquid B was there in the tin? What quantity does the tin hold?
Options- A. 58 l
- B. 65 l
- C. 50 l
- D. 62 l Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 50 l
Explanation:
Let the tin contain 5x litres of liquids
=> 5(4x - 36) = 2(x + 36)
=> 20x - 180 = 2x + 72
=> x = 14 litres
Hence, the initial quantity of mixture = 70l
Quantity of liquid B
=
= 50 litres.
- 7. In a mixture of milk and water the proportion of water by weight was 75%. If in 60 gm of mixture 15 gm water was added, what would be the percentage of water? (Weight in gm)
Options- A. 80%
- B. 70%
- C. 75%
- D. 62% Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 80%
Explanation:
Water in 60 gm mixture=60 x 75/100 = 45 gm. and Milk = 15 gm.
After adding 15 gm. of water in mixture, total water = 45 + 15 = 60 gm and weight of a mixture = 60 + 15 = 75 gm.
So % of water = 100 x 60/75 = 80%.
- 8. In a 48 ltr mixture, the ratio of milk and water is 5:3. How much water should be added in the mixture so as the ratio will become 3:5?
Options- A. 24 lit
- B. 16 lit
- C. 32 lit
- D. 8 lit Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 32 lit
Explanation:
Given mixture = 48 lit
Milk in it = 48 x 5/8 = 30 lit
=> Water in it = 48 - 30 = 18 lit
Let 'L' lit of water is added to make the ratio as 3:5
=> 30/(18+L) = 3/5
=> 150 = 54 + 3L
=> L = 32 lit.
- 9. 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 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
or
Therefore, K = 1250
Hence initially the honey in the jar= 1.25 kg
- 10. A man pays Rs. 6.40 per litre of milk. He adds water and sells the mixture at Rs. 8 per litre, thereby making 37.5% profit. The proportion of water to milk received by the customers is
Options- A. 1 : 10
- B. 10 : 1
- C. 9 : 11
- D. 11 : 9 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 1 : 10
Explanation:
Customer ratio of Milk and Water is given by
Milk :: Water
6.4 0
=> Milk : Water = 110 : 11 = 10 : 1
Therefore, the proportionate of Water to Milk for Customer is 1 : 10
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