Exercise : Alligation or Mixture - General Questions
✔ Alligation or Mixture -
General Questions
11.
A container contains 40 liters of milk. From this, 4 liters are taken out and replaced by water. This process is repeated two more times. How much milk is now in the container?
View Answer
Answer: Option A
Explanation:
Explanation:
Final Milk = \(P(1 - y/x)^n = 40(1 - 4/40)^3 = 40(0.9)^3 = 40 \times 0.729 = 29.16\) liters.
12.
In what ratio must three types of wheat at \(12, \)14, and \(20 per kg be mixed to produce a mixture worth \)15 per kg?
View Answer
Answer: Option A
Explanation:
Explanation:
Pair (12, 20) for 15 gives 5:3. Pair (14, 20) for 15 gives 5:1. Combined ratio: Wheat 1 = 5, Wheat 2 = 5, Wheat 3 = \(3 + 1 = 4\). Ratio = 5:5:4.
13.
Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?
View Answer
Answer: Option A
Explanation:
Explanation:
Ratio = \((15 - 9) : (19 - 15) = 6 : 4 = 3 : 2\).
14.
A jar full of whiskey contains 40% alcohol. A part of this is replaced by another containing 19% alcohol and the percentage of alcohol was found to be 26%. What quantity was replaced?
View Answer
Answer: Option A
Explanation:
Explanation:
Ratio (Original : Replacement) = \((26 - 19) : (40 - 26) = 7 : 14 = 1 : 2\). Total volume = 3 units. Quantity replaced = 2/3.
15.
A sum of $6.40 is made up of 80 coins which are either 10-paise or 5-paise coins. How many are 5-paise coins?
View Answer
Answer: Option A
Explanation:
Explanation:
Average value per coin = \(640 / 80 = 8\) paise. Ratio (10p : 5p) = \((8 - 5) : (10 - 8) = 3 : 2\). 5-paise coins = \((2 / 5) \times 80 = 32\) coins.
16.
Two alloys contain tin and iron in ratios 1:2 and 2:3. If these are mixed in the ratio 3:4, what is the ratio of tin to iron in the new alloy?
View Answer
Answer: Option A
Explanation:
Explanation:
Tin = \(3(1/3) + 4(2/5) = 2.6\). Iron = \(3(2/3) + 4(3/5) = 4.4\). Ratio = \(2.6 : 4.4 = 13 : 22\).
17.
A person has a chemical of $25 per liter. In what ratio should water be mixed with it so that by selling at $20 per liter he may get 25% profit?
View Answer
Answer: Option A
Explanation:
Explanation:
CP of mixture = \(20 / 1.25 = 16\). Cost of Water = 0. Ratio (Water : Chemical) = \((25 - 16) : (16 - 0) = 9 : 16\).
18.
8 liters are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left to that of water is 16 : 65. How much wine did the cask hold originally?
View Answer
Answer: Option A
Explanation:
Explanation:
Final Wine / Total Volume = \(16 / 81\). \((1 - 8/x)^4 = 16/81 \implies 1 - 8/x = 2/3 \implies 8/x = 1/3 \implies x = 24\) liters.
19.
A milkman steals milk from a can and replaces it with water. He does this twice. After two such operations, the ratio of milk to water is 9:7. What percentage of the milk was replaced each time?
View Answer
Answer: Option A
Explanation:
Explanation:
Final Milk / Total Volume = \(9 / 16\). \((1 - k)^2 = 9/16 \implies 1 - k = 3/4 \implies k = 1/4 = 25\%\).
20.
Vessel A contains milk and water in ratio 4:5 and vessel B in 5:1. In what ratio must liquid from A and B be mixed so that the new mixture contains milk and water in ratio 5:4?
View Answer
Answer: Option A
Explanation:
Explanation:
Milk in A = \(4/9\), B = \(5/6\), Result = \(5/9\). Difference 1 = \(5/6 - 5/9 = 5/18\). Difference 2 = \(5/9 - 4/9 = 1/9\). Ratio = \(5/18 : 1/9 = 5 : 2\).