Alligation or Mixture problems
- 1. 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.
- 2. 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: CAT, GATE, Analyst, Bank Clerk, Bank PO, AIEEE, Bank Exams
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
- 3. A mixture contains 25% milk and rest water. What percent of this mixture must taken out and replaced with milk so that in mixture milk and water may become equal.
Options- A. 31.8%
- B. 31%
- C. 33.33%
- D. 29.85% Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 33.33%
Explanation:
Now, take percentage of milk and applying mixture rule
25 100
50
50 25 = 2 : 1
Hence required answer = 1/3 or 33.33%
- 4. A container contains 50 litres of milk. From that 8 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container ?
Options- A. 24.52 litres
- B. 29.63 litres
- C. 28.21 litres
- D. 25.14 litres Also asked in: CAT, Bank PO
Correct Answer: 29.63 litres
Explanation:
Given that container has 50 litres of milk.
After replacing 8 litres of milk with water for three times, milk contained in the container is:
= 29.63 litres.
- 5. A milkman claims to sell milk at its cost price, still, he is making a profit of 30% since he has mixed some amount of water in the milk. What is the % of milk in the mixture?
Options- A. 71.02%
- B. 76.92%
- C. 63.22%
- D. 86.42% Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 76.92%
Explanation:
Let the milk he bought is 1000 ml
Let C.P of 1000 ml is Rs. 100
Here let he is mixing K ml of water
He is getting 30% profit
=> Now, the selling price is also Rs. 100 for 1000 ml
=> 100 : K%
= 100 : 30
10 : 3 is ratio of milk to water
=> Percentage of milk = 10 x 100/13 = 1000/13 = 76.92%
- 6. 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
- 7. 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 =
- 8. 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.
- 9. 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.
- 10. 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
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