Exercise : Alligation or Mixture - General Questions
✔ Alligation or Mixture -
General Questions
1.
In what ratio must rice at $62 per kg be mixed with rice at $72 per kg so that the mixture is worth $67 per kg?
View Answer
Answer: Option A
Explanation:
Explanation:
Using the Alligation Rule: Ratio = \((D - M) : (M - C)\).
Here, \(D = 72\), \(C = 62\), and \(M = 67\).
Ratio = \((72 - 67) : (67 - 62) = 5 : 5 = 1 : 1\).
Here, \(D = 72\), \(C = 62\), and \(M = 67\).
Ratio = \((72 - 67) : (67 - 62) = 5 : 5 = 1 : 1\).
2.
A mixture contains milk and water in the ratio 4:1. If the total volume is 20 liters, find the quantity of water.
View Answer
Answer: Option B
Explanation:
Explanation:
Total parts = \(4 + 1 = 5\). Quantity of water = \((\text{Water ratio} / \text{Total ratio}) \times \text{Total volume} = (1 / 5) \times 20 = 4\) liters.
3.
In what ratio must tea at $120/kg be mixed with tea at $150/kg so that the blended tea is worth $140/kg?
View Answer
Answer: Option A
Explanation:
Explanation:
Difference between Dearer and Mean = \(150 - 140 = 10\). Difference between Mean and Cheaper = \(140 - 120 = 20\). Ratio = \(10 : 20 = 1 : 2\).
4.
A 30-liter mixture of milk and water has milk and water in ratio 7:3. How much water is in it?
View Answer
Answer: Option A
Explanation:
Explanation:
Total ratio = \(7 + 3 = 10\). Water = \((3 / 10) \times 30 = 9\) liters.
5.
In what ratio must water be mixed with milk to gain 20% by selling the mixture at cost price?
View Answer
Answer: Option A
Explanation:
Explanation:
To gain \(x\%\), the ratio of Water to Milk must be \(x : 100\). Ratio = \(20 : 100 = 1 : 5\).
6.
A merchant has 100 kg of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10% on the whole. Find the quantity sold at 17%.
View Answer
Answer: Option A
Explanation:
Explanation:
Ratio = \((17 - 10) : (10 - 7) = 7 : 3\). Total weight = 100 kg. Quantity at 17% = \((3 / 10) \times 100 = 30\) kg.
7.
How many kg of salt at 42 paise/kg must a man mix with 25 kg of salt at 24 paise/kg so that he may, on selling the mixture at 40 paise/kg, gain 25%?
View Answer
Answer: Option A
Explanation:
Explanation:
CP of mixture = \(40 / 1.25 = 32\) paise. Ratio (42p : 24p) = \((32 - 24) : (42 - 32) = 8 : 10 = 4 : 5\). Since 5 units = 25 kg, 1 unit = 5 kg. Required salt (4 units) = \(4 \times 5 = 20\) kg.
8.
In a 40-liter mixture, the ratio of milk to water is 3:1. How much water must be added to make the ratio 2:1?
View Answer
Answer: Option A
Explanation:
Explanation:
Milk = 30L, Water = 10L. Let \(x\) be water added: \(30 / (10 + x) = 2 / 1 \implies 30 = 20 + 2x \implies 2x = 10 \implies x = 5\) liters.
9.
Two vessels A and B contain milk and water in ratios 5:2 and 8:5. In what ratio should these be mixed to get a mixture with milk and water in ratio 9:4?
View Answer
Answer: Option A
Explanation:
Explanation:
Fraction of milk in A = \(5/7\), B = \(8/13\), Result = \(9/13\). Ratio = \((9/13 - 8/13) : (5/7 - 9/13) = 1/13 : 2/91 = 7 : 2\).
10.
A mixture of 70 liters of fruit juice and water contains 10% water. How many liters of water should be added to make it 12.5% water?
View Answer
Answer: Option A
Explanation:
Explanation:
Current water = 7L, Juice = 63L. Let \(x\) be water added. \((7 + x) / (70 + x) = 1/8 \implies 56 + 8x = 70 + x \implies 7x = 14 \implies x = 2\) liters.