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- Question
- Two vessels A and B contain mixture of milk and water in the ratio 4 : 1 and 9 : 11 respectively. They are mixed in the ratio of 3 : 2. Find the ratio of milk and water in the resulting mixture.
Options- A. 34 : 16
- B. 33 : 17
- C. 16 : 34
- D. 17 : 33
- Correct Answer
- 33 : 17
Explanation
- 1. A shopkeeper buys 26 liter of milk @ Rs. 16 per liter. He also buys from another source an inferior quality of milk @ Rs. 10 per liter. How much quantity of the later should he buy to mix it with the former so that he can sell the mixture @ Rs. 14 per liter without making any loss?
Options- A. 13 liter
- B. 12 liter
- C. 14 liter
- D. 16 liter Discuss
- 2. 640 ml of a mixture contains milk and water in ratio 6:2. How much of the water is to be added to get a new mixture containing half milk and half water?
Options- A. 310 ml
- B. 320 ml
- C. 330 ml
- D. 340 ml Discuss
- 3. A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
Options- A. 5:3
- B. 1:4
- C. 4:1
- D. 9:1 Discuss
- 4. In what ratio must a grocer mix sugar at 72 paise per kg with sugar at 48 paise per kg. So that by selling the mixture at
63 paise per kg he may gain 1 of his out-lay? 6
Options- A. 1 : 3
- B. 3 : 1
- C. 2 : 3
- D. 3 : 2 Discuss
- 5. A dishonest milkman professes to sell his milk at C. P. But he mixes it with water and thereby gains 25 %. The % of water in the mixture is ?
Options- A. 25%
- B. 20%
- C. 4%
- D. None of these Discuss
- 6. 6 liters of milk and water mixture has 75% milk in it. How much milk should be added to the mixture to make it 90% pure?
Options- A. 8 liters
- B. 9 liters
- C. 10 liters
- D. 12 liters Discuss
- 7. In what ratio must water be added to spirit to gain 25% by selling it at cost price?
Options- A. 1 : 4
- B. 4 : 1
- C. 3 : 4
- D. 4 : 3 Discuss
- 8. A shopkeeper has 50 kgs of rice. He sells a part of it at 20% profit and the rest at 40% profit. If he gains 25% on the whole, find the quantity of each part.
Options- A. 12.5 kgs and 37.5 kgs
- B. 37.5 kgs and 12.5 kgs
- C. 23.5 kgs and 21.5 kgs
- D. 21.5 kgs and 23.5 kgs Discuss
- 9. The average monthly salary of employees, consisting of officers and workers, of an organisation is Rs. 3000. The average salary of an officer is Rs. 10,000 while that of a worker is Rs. 2000 per month. If there are total 400 employees in the organisation, find the number of officers and workers separately.
Options- A. 300 , 100
- B. 50 , 350
- C. 250 , 150
- D. 310 , 90 Discuss
- 10. If 4 kg of an alloy made of 1/4th iron and rest is mixed with 6 kg of another alloy made of 2/3rd iron and rest tin, find the ratio of iron to tin in the resultant mixture.
Options- A. 1 : 1
- B. 2 : 1
- C. 1 : 2
- D. 3 : 2 Discuss
Alligation or Mixture problems
Search Results
Correct Answer: 13 liter
Explanation:
Quantity of milk @ Rs.10 per liter / Quantity of milk @ Rs. 16 per liter = 1 / 2
So, quantity of milk @ Rs. 10 per liter = 26 / 2 = 13 liter.
2nd Method
Let us assume shopkeeper buy P liter milk of price @ Rs. 10 per liter.
Buy price of 26 liter of milk @ Rs. 16 per liter = 26 x 16
Buy price of P liter of milk @ Rs. 10 per liter = P x 10
Sell price of total milk ( P + 26 ) @ Rs. 14 per liter = 14 x ( P + 26 )
According to question there is no loss or no profit.
Then Buy Price = Sell Price
26 x 16 + P x 10 = 14 x ( P + 26 )
? 26 x 16 + 10P = 14P + 14 x 26
? 26 x 16 - 26 x 14 = 14P - 10P
? 2 x 26 = 4P
? 4P = 2 x 26
? P = 2 x 26 / 4 = 13
So, quantity of milk @ Rs. 10 per liter = 13 liter.
Correct Answer: 320 ml
Explanation:
Let us assume the ratio product is Q.
According to question,
Quantity of Milk in mixture = 6Q ml
Quantity of Water in mixture = 2Q ml
Quantity of Milk in mixture + Quantity of Water in mixture = 640
6Q + 2Q = 640
8Q = 640
Q = 640/8
Q = 80
Quantity of Milk in mixture = 6Q ml = 6 x 80 = 480 ml
Quantity of Water in mixture = 2Q ml = 2 x 80 = 160 ml
To find the new mixture containing half milk and half water,
Quantity of water to be added for making the mixture of equal quantity of milk and water = 480 - 160 = 320
Correct Answer: 9:1
Explanation:
According to question,
Quantity of Milk/Quantity of Water = 3/2
Let us assume the product ratio = n.
Quantity of Milk = 3n and Quantity of Water = 2n liters
Quantity of Milk + Quantity of Water = 20 liters
3n + 2n = 20 liters
5n = 20 liters
n = 20/5
n = 4
Quantity of Milk = 3n liters
Put the value of n,
Quantity of Milk = 3 x 4 = 12 liters
Quantity of Water = 2n
Quantity of Water = 2 x 4 = 8 liters
If 10 liters of mixture are removed first time, we will find how much milk and water contain in mixture.
? 20 liters of mixture contains 12 liter of milk.
? 1 liters of mixture contains 12/20 liter of milk.
? 10 liters of mixture contains 10 x 12/20 liter of milk.
? 10 liters of mixture contains 6 liter of milk.
? 10 liters of mixture contains 4 liter of water.
If 10 liters of mixture are removed, then amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters and water = 4 liters.
If the process is repeated one more time and 10 liters of the mixture are removed second time, then
If 10 liters of mixture are removed, Again we will find how much milk and water contain in the mixture.
? 20 liters of mixture contains 16 liter of milk.
? 1 liters of mixture contains 16/20 liter of milk.
? 10 liters of mixture contains 10 x 16/20 liter of milk.
? 10 liters of mixture contains 8 liter of milk.
? 10 liters of mixture contains 2 liter of water.
If 10 liters of mixture are removed, then amount of milk removed = 8 liters and amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 - 2) = 2 liters.
Now 10 liters milk is added => total milk = 18 liters and water will be 2 liters.
The required ratio of milk and water in the final mixture obtained
Quantity of milk/Quantity of Water= 18:2 = 9:1
Correct Answer: 1 : 3
Explanation:
Correct Answer: 20%
Explanation:
Correct Answer: 9 liters
Explanation:
The given solution has 75% milk.
Milk to be added has 100% milk.
Milk should be added to the given mixture in the ratio 15 : 10 or 3 : 2
? Quantity of milk to be added = (3 / 2) × 6 = 9 liters.
Correct Answer: 1 : 4
Explanation:
Let cost price of spirit be Re. 1 per liter.
Then SP of mixture = Re. 1 per liter
Gain = 25%
So, CP of mixture = 1 × (100 / 125) = Re. 4 / 5
We assume that CP of water is zero.
Using allegation rule on cost price,
Water should be mixed to spirit in the ratio (1 / 5) : (4 / 5) or 1 : 4
Correct Answer: 37.5 kgs and 12.5 kgs
Explanation:
According to figure we find that the ratio will be 3 : 1.
Quantity sold at 20% profit = 3 / (3 + 1) × 50 = 37.5 kgs.
Quantity sold at 40% profit = (50 ? 37.5) = 12.5 kgs.
Correct Answer: 50 , 350
Explanation:
As per figure we can calculate the ration as below
Number of officers / Number of workers = 1000 / 7000 = 1 / 7
No. of officers = 1 / (1 + 7) × 400 = 50
No. of workers = 400 ? 50 = 350
Correct Answer: 1 : 1
Explanation:
Total quantity of iron = 4 (1 / 4) + 6 (2 / 3) = 1 + 4 = 5 kg.
Total quantity of tin = (4 + 6) ? 5 = 5 kg.
In the resultant mixture, iron : tin = 5 : 5 or 1 : 1
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