Alligation or Mixture problems
- 1. The average age of 6 members of a family is 20 years. If the age of the servant is included, then the average age increase by 25%. What is the age (in years) of the servant?
Options- A. 30
- B. 35
- C. 50
- D. 55 Also asked in: Bank Exams
Correct Answer: 55
Explanation:
Ratio of milk and water = 2 : 1
Quantity of milk = 60 X 2/3 = 40 litre
Quantity of water = 20 litre
To make ratio, 1: 2, we have to double the water that of milk
So, water should be 80 litre.
That means 80 ? 20 = 60 litre water to be added.
- 2. In a triangle XYZ , which of the following conditions is true
Options- A. XY YZ > ZX
- B. XY + YZ < ZX
- C. XY YZ < XZ
- D. XY + ZX < YZ Also asked in: Bank Exams
Correct Answer: XY YZ < XZ
Explanation:
Ratio of milk and water = 2 : 1
Quantity of milk = 60 X 2/3 = 40 litre
Quantity of water = 20 litre
To make ratio, 1: 2, we have to double the water that of milk
So, water should be 80 litre.
That means 80 ? 20 = 60 litre water to be added.
- 3. In what ratio sugar of Rs 38 per kg and Rs 30 per kg be mixed with each other so that on selling mixture at Rs 35.2 per kg there will be a profit of 10%?
Options- A. 1 : 3
- B. 3 : 7
- C. 13 : 7
- D. 9 : 4 Also asked in: Bank Exams
Correct Answer: 1 : 3
Explanation:
Ratio of milk and water = 2 : 1
Quantity of milk = 60 X 2/3 = 40 litre
Quantity of water = 20 litre
To make ratio, 1: 2, we have to double the water that of milk
So, water should be 80 litre.
That means 80 ? 20 = 60 litre water to be added.
- 4. In what ratio must a mixture of 20% milk strength be mixed with that of 60% milk strength so as to get a new mixture of 25% milk strength?
Options- A. 7 : 1
- B. 4 : 1
- C. 5 : 2
- D. 9 : 2 Also asked in: Bank Exams
Correct Answer: 7 : 1
Explanation:
Ratio of milk and water = 2 : 1
Quantity of milk = 60 X 2/3 = 40 litre
Quantity of water = 20 litre
To make ratio, 1: 2, we have to double the water that of milk
So, water should be 80 litre.
That means 80 ? 20 = 60 litre water to be added.
- 5. A mixture contains spirit and water in the ratio of 3 : 2. If it contains 3 litres more spirit than water, the quantity of spirit in the mixture is
Options- A. 12 litres
- B. 10 litres
- C. 9 litres
- D. 8 litres Also asked in: Bank Exams
Correct Answer: 9 litres
Explanation:
Ratio of milk and water = 2 : 1
Quantity of milk = 60 X 2/3 = 40 litre
Quantity of water = 20 litre
To make ratio, 1: 2, we have to double the water that of milk
So, water should be 80 litre.
That means 80 ? 20 = 60 litre water to be added.
- 6. A man bought a certain quantity of sugar for Rs. 8000. He sells one-fourth of it at 20% loss. At what per cent profit should he sell the remainder stock so as to make an overall profit of 20%?
Options- A. 20%
- B. 30%
- C. 35%
- D. 40% Also asked in: Bank Exams
Correct Answer: 30%
Explanation:
Let the remainder stock be sold at P% profit.
(P - 20) / 30 = ((1 / 4) / (3 / 4))
or (P ? 20) = 30 × (1 / 3)
or P = 20 + 10
P = 30% profit.
- 7. 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 Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
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
- 8. Tea worth of Rs. 135/kg & Rs. 126/kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be____?
Options- A. Rs. 169.50
- B. Rs.1700
- C. Rs. 175.50
- D. Rs. 180 Also asked in: CAT, Bank Exams, AIEEE
Correct Answer: Rs. 175.50
- 9. 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
- 10. 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
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