mixtures and alligation practice problems with solutions

Question 1: In what proportion must tea at Rs. 7.50 per kg be mixed with tea at Rs. 10.50 per kg to produce a mixture worth Rs. 8.50 per kg?
[A] 1 : 2
[B] 2 : 1
[C] 1 : 1
[D] 2 : 3
Option: 2

Solution :

Using the formula of alligation,

 required ratio =2: 1

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Question 2: Metal A costs Rs. 8.40 per gm and Metal B Rs. 0.21 per gm. In what proportion must these metals be mixed so that gram of the mixture may be worth Rs. 5.67?
[A] 1 : 2
[B] 1 : 3
[C] 2 : 1
[D] 2 : 3
Option: 3

Solution :

Using the formula of alligation,

required ratio= 2: 1 

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Question 3: A 15-litre mixture contains 20% alcohol and the rest water. If 3 litres of water is mixed in it, then the percentage of alcohol in the new mixture will be
[A] 17%
[B]
[C]
[D] 15%
Option: 2

Solution :

Initially, the mixture contains 3 litres of alcohol and 12 litres of water. Afterwards, the mixture contains 3 litres of alcohol and 15 litres of water.

percentage of alcohol.

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Question 4: A mixture of 20 kg of water and spirit contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%?
[A] 4 kg
[B] 5 kg
[C] 8 kg
[D] 30 kg
Option: 1

Solution :

Water

In the second mixture:

75 kg spirit is contained in a mixture of 100 kg

18 kg spirit is contained in a mixture of.

So, water to be added=24-20=4 kg

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Question 5: A sum of money is sufficient to pay Sachin’s salary of 45 days and kale’s salary for 60 days. For how many days can the sum pay the salary of both?
[A] 25 days
[B] 280/11 days
[C] 180/7 days
[D] 270/11 days
Option: 3

Solution :

Sachin's salary for one day =  1/45th of the sum of money.

For kale's salary for one day = 1/60 of the sum of money.

=> (Sachin + kale)'s salary for one day= 1/45+1/60=7/180th of the sum.

Hence, when they both work together, the sun will last for 180/7 days.

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Question 6: A grocer buys two kinds of rice at Rs. 1.80 and Rs. 1.20 per kg respectively. In what proportion should these be mixed, so that by selling the mixture at Rs. 1.75 per kg 25% may be gained?
[A] 2 : 1
[B] 3 : 2
[C] 3 : 4
[D] 1 : 2
Option: 4

Solution :

S.P. Of 1 kg mixture =  Rs. 1.75,  gain= 25%.

Mean price= Rs.

(Dearer price) : (cheaper price)=20:40=1:2.

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Question 7: A and B are two alloys of iron and silver prepared by mixing metals in the ratio 4 : 5 and 7 : 5 respectively. If equal quantities of alloys are melted to form a third alloy C, the ratio of iron to silver in C is
[A] 37 : 35
[B] 19 : 18
[C] 31 : 25
[D] 29 : 35
Option: 1

Solution :

In alloy A, the ratio of iron to Silver=4:5, 5+4=9

In alloy B, the ratio of iron to Silver=7:5, 7+5=12, as the amount to be mixed.

So take the LCM of 9 and 12.  hence, we mix 36  gm of A and 36  gm of B.

(the reason for choosing LCM as the amount is to simplify calculations.)

For a: amount of iron= And amount of silver=

For B: amount of iron=And amount of silver=

Hence, Total amount of iron=16+21=37

Total amount of silver=20+15=35

 Hence, Final ratio of iron to Silver in the mix of two alloys= 37:35

Shortcut: Required ratio is

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Question 8: The ratio of milk and water in 66 kg of adultered milk is 5 : 1. Water is added to make the ratio 5 : 3. The quantity of water added is
[A] 22 kg
[B] 24.7 5kg
[C] 16.50 kg
[D] 20 kg
Option: 1

Solution :

In the first mixture

Milk=

Water=11kg

In the second mixture

If milk is 55kg, then water

Water to be added= 55-33=22kg

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Question 9: Mixture of alcohol and water contains 35% of alcohol by volume. Then, 40 ml of water is added to such a mixture of 100 ml. The percentage of alcohol in the new mixture is
[A] 30%
[B] 35%
[C] 25%
[D] 20%
Option: 3

Solution :

Here percentage alcohol in the mixture is to be found out. So, the quantity of alcoholis kept as numerator

 (since 40 ml water is added

Quantity of mixture=100+40).

% alcohol

 the mixture contains 20% alcohol.

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Question 10: A mixture, 729 ml in volume, contains milk and water in the ratio 7: 2. How much more water is to be added to get a new mixture containing milk and water in the ratio 7: 3?
[A] 600 ml
[B] 710 ml
[C] 520 ml
[D] None of   these
Option: 4

Solution :

Milk

Water=729-167=162 ml.

 Let X ml of water be added

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Question 11: A mixture of 24 litres contains water and milk in the ratio 3: 5. How much water must be added to this mixture to reverse the ratio?
[A] 20 litres
[B] 24 litres
[C] 18 litres
[D] 16 litres
Option: 4

Solution :

 let X litre of water be added, initial quantity of water 3/8  x 24  =  9.

X=16 litres.

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Question 12: A trader mixes two varieties of tea costing Rs 40 per kg and rupees 50 per kg in the ratio 5: 4. If the mixture is sold at rupees 48 per kg question, then what is the gain percentage?
[A] 7.5 %
[B] 8%
[C] 2.5 %
[D] 5%
Option: 2

Solution :

 let the quantities of two varieties of tea be "5X" kg and "4X" kg respectively.

Thus, cost price..… (1)

and sales price …..  (2)

Profit=(2)-(1)=Rs. 32x

profit %

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Question 13: Two containers of equal volume contains milk and water in the ratio 3: 5 and 5: 3, respectively. If the contents of both containers are emptied into a third one, what would be the ratio of milk to water in that container?
[A] 1: 1
[B] 9: 25
[C] 25: 9
[D] None of these
Option: 1

Solution :

Let the volume of both the container b x units each. Thus, the first container would containunits of milk andunits of water, whereas the second container would containunits of milk andunits of water. When the content of both are empty into a third one it would have,

Milk                               …(1)

And water                     ….(2)

Thus, the required  ratio.

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Question 14: From two ornament Weighing 18 gram and 24 gram containing gold and silver in the ratio of 2: 1 and 5: 1 respectively, a new ornament is made. What is the amount of gold in the new ornament?
[A] 10 gram
[B] 12 gram
[C] 32 gram
[D] 28 gram
Option: 3

Solution :

 from the first ornament, gold

From the second ornament gold

Thus, total gold=32 gm.

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Question 15: A and B are two alloys of gold and copper prepared by mixing metals in proportions 5: 3 and 5: 11 respectively. If equal quantities of this alloys are melted to a third alloy C, what would be the proportion of gold and copper in the alloys thus formed?
[A] 25: 33
[B] 33: 25
[C] 15: 17
[D] 17: 15
Option: 3

Solution :

 required proportion of gold and silver is 

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