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Alligation and Mixture Aptitude Test Paper 1

1) A 60 liter mixture of milk and water contains 10% water. How much water must be added to make water 20% in the mixture?

1. 8 liters
2. 7.5 liters
3. 7 liters
4. 6.5 liters

The Correct answer is (B)

Answer with explanation:

The mixture has 10% water, so the milk would be 90% of 60 liters.

Milk = * 60 = 54 liters
Â Â Â Â Â Â Â Â Â Â Â Â 100Â Â Â Â Â Â Â Â

âˆ´Water = 60 â€“ 54 = 6 liters

Let water to be added = x liters

Now, Â Â 6+xÂ Â * 100 = 20
Â Â Â Â Â Â Â Â Â Â Â 60+xÂ Â Â Â Â Â Â

Â Â 6+xÂ Â =Â Â Â Â 1Â Â
Â Â 60+xÂ Â Â Â Â Â 5Â Â

30 + 5x = 60+x

30 â€“ 60 = x â€“ 5x

â€“ 30 = â€“ 4x

x =30Â Â =7.5 liters
Â Â Â Â Â Â 4Â Â Â Â Â

2) An alloy contains14 parts of tin and 100 parts of copper. What is the percentage of tin in the alloy ?

1. 12.3%
2. 13%
3. 11.5%
4. 11%

The Correct answer is (A)

Answer with explanation:

In 114 parts of alloy, tin = 14 parts

âˆ´Percentage of tin =Â Â 14Â Â âˆ—100=12.3%
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 114Â Â Â Â Â Â Â Â

3) A 20 liter mixture contains 30% alcohol and 70% water. If 5 liters of water is added to the mixture, what will be the percentage of alcohol in the new mixture ?

1. 22%
2. 23%
3. 24%
4. 25%

The Correct answer is (C)

Answer with explanation:

Initially, the mixture contains 30% alcohol =Â Â 30 âˆ—20=6 liters of alchol
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 100Â Â Â Â Â Â Â Â

And, 70% of water =Â Â 70 âˆ—20=14 liters of water
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 100Â Â Â Â Â Â Â Â

After adding 5 liters of water, the mixture contains (14+5) 19 liters of water and 6 liters of alcohol.

âˆ´Percentage of alcohol = 6 âˆ—100=24%
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 25

4) In what ratio water must be mixed with milk costing Rs. 48 per liter to get a mixture worth Rs. 32 per liter ?

1. 2:3
2. 3:2
3. 3:4
4. 1:2

The Correct answer is (D)

Answer with explanation:

Apply alligation rule:

âˆ´ Water = 16 = 1
Â Â Â Â MilkÂ Â Â Â Â 32Â Â Â Â 2Â

Required ratio; water:milk = 1:2

5) A shopkeeper mixes 60 kg of sugar worth Rs. 30 per kg with 90 kg of sugar worth Rs. 40 per kg. At what rate he must sell the mixture to gain 20%?

1. Rs. 30 per kg
2. Rs. 34 per kg
3. Rs. 43.2 per kg
4. Rs. 38 per kg

The Correct answer is (C)

Answer with explanation:

Total cost price of (60+90)150 kg of mixture = (60*30+90*40)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 1800+3600

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = Rs. 5400

Cost Price per kg of mixture = 5400 = Rs. 36 per kg
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 150

Now, Required gain = 20%

âˆ´Required selling price per kg of mixture = 120 âˆ—36 = Rs. 43.2 per kg
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 100