Alligation or Mixture
- The ratio of milk and water in 66 kg of adulterated milk is 5 : 1. Water is added to it to make the ratio 5 : 3. The quantity of water added is —
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Here , Ratio of of milk and water in 66 kg of adulterated milk = 5 : 1
In first mixture :Milk = 
66 × 5 
= 55 kg 6
and water = 11 kg
In second mixture :
Ratio = 5 : 3If milk is 55 kg then water = 3 × 55 5
Correct Option: A
Here , Ratio of of milk and water in 66 kg of adulterated milk = 5 : 1
In first mixture :Milk = 66 × 5 = 55 kg 6
and water = 11 kg
In second mixture :
Ratio = 5 : 3
New quantity of water = 33 kgIf milk is 55 kg then water = 3 × 55 5
∴ Water to be added = 33 - 11 = 22 kg.
- Two vessels A and B contains milk and water mixed in the ratio 5 : 3 and 2 : 3. When these mixtures are mixed to form a new mixture containing half milk and half water, they must be taken in the ratio —
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As per the given question , we can say that
Milk in A = 5 of whole, Milk in B = 2 of whole, 8 5 Milk in mixture of A and B = 1 2
∵ By alligation rule ,Correct Option: C
As per the given question , we can say that
Milk in A = 5 of whole, Milk in B = 2 of whole, 8 5 Milk in mixture of A and B = 1 2
∵ By alligation rule ,(Mix. in A) : (Mix. in B) = 1 : 1 10 8
(Mix. in A) : (Mix. in B) = 4 : 5
- In a mixture of 60 liters, the ratio of milk and water is 2 : 1. If the ratio of the milk and water is to be 1 : 2, then the amount of water to be further added is —
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Here , mixture of 60 litres, the ratio of milk and water is 2 : 1.
Required answer = 60 200 - 100 litres. 3 3 100 - 200 3 Correct Option: D
Here , mixture of 60 litres, the ratio of milk and water is 2 : 1.
Hence , The amount of water to be further added is 60 ml .Required answer = 60 200 - 100 = 60 litres. 3 3 100 - 200 3
- How much chicory at Rs. 24 a kg should be added to 15 kg of tea at Rs. 60 a kg as to make the mixture worth Rs. 39 a kg ?
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Given that :- C1 = Rs. 60 , C2 = Rs. 24 and Mean cost Price ( M ) = Rs. 39
By alligation method :
∴ Ratio of tea and chicori = 5 : 7
Correct Option: A
Given that :- C1 = Rs. 60 , C2 = Rs. 24 and Mean cost Price ( M ) = Rs. 39
By alligation method :
∴ Ratio of tea and chicori = 5 : 7∴ Added chicori = 15 × 7 = 21 kg 5 
- 4 vessels of equal sizes contains mixture of spirit and water. The concentration of spirit in 4 vessels are 60 %, 70 %, 75 % and 80 % respectively. If all the 4 mixtures are mixed, find in the resultant mixture the ratio of spirit to water —
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Given : - The concentration of spirit in 4 vessels are 60%, 70%, 75% and 80% respectively.
Ratio of spirit to water in the different vessels⇒ 60 = 3 : 2, 75 = 3 : 1, 40 25 70 = 7 : 3, 80 = 4 : 1 30 20
Now, applying the given rule,we have the required ratio = 3 + 7 + 3 + 4 : 2 + 3 + 1 + 1 5 10 4 5 5 10 4 5
Correct Option: C
Given : - The concentration of spirit in 4 vessels are 60%, 70%, 75% and 80% respectively.
Ratio of spirit to water in the different vessels⇒ 60 = 3 : 2, 75 = 3 : 1, 40 25 70 = 7 : 3, 80 = 4 : 1 30 20
Now, applying the given rule,we have the required ratio = 3 + 7 + 3 + 4 : 2 + 3 + 1 + 1 5 10 4 5 5 10 4 5 Required ratio = 12 + 14 + 15 + 16 : 6 + 6 + 5 + 4 20 20
Required ratio = 57 : 23.
