Alligation or Mixture
- A can contains a mixture of 2 liquids A and B in proportion 7 : 5 when 9 liters of mixture are drawn off and the can is filled with B, the proportion of A and B becomes 7 : 9. How many liters of liquid A was contained by the can initially ?
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Let the can initially contain 7y litres and 5y litre of mixtures A and B respectively. Thus out of 12y litre of total mixture, 9 litre were taken out.
Quantity of A in mix. left = 
7y - 9 × 7y 
28y - 21 litres 12x 4 Quantity of B in mix. left = 5y - 9 × 5y 12x
According to question ,Quantity of B in mix. left = 20y - 15 litres 4 ∴ 28y - 21 : 20y - 15 + 9 :: ( 7 : 9 ) 4 4 Correct Option: D
Let the can initially contain 7y litres and 5y litre of mixtures A and B respectively. Thus out of 12y litre of total mixture, 9 litre were taken out.
Quantity of A in mix. left = 7y - 9 × 7y 28y - 21 litres 12x 4 Quantity of B in mix. left = 5y - 9 × 5y 12x
According to question ,Quantity of B in mix. left = 20y - 15 litres 4
⇒ y = 3∴ 28y - 21 : 20y - 15 + 9 :: ( 7 : 9 ) 4 4
Hence , Required answer 7y = 7 x 3 = 21 litre.
- How many bananas at 5 for Re. 1·20 should be mixed with 300 bananas at 6 for Rs. 2·10, so that they should all be worth Rs. 3·60 a dozen ?
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By the alligation rule ,
Correct Option: D
∴ Required answer = 300 × 5 = 250 6
By the alligation rule ,
- A milk seller pays Rs. 500 per kiloliter for his milk. He adds water to it and sells the mixture at 56 P a liter, thereby making altogether 40 % profit. Find the proportion of water to milk which his customers receive ?
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Here , a = 500 = 50 P, b = 56 P, Profit % = 40% 1000 Ratio of milk to water = 56 (50 – 56) + 40 × 50 100 Ratio of milk to water = 4 = 4 : 1 1
Correct Option: A
Here , a = 500 = 50 P, b = 56 P, Profit % = 40% 1000 Ratio of milk to water = 56 (50 – 56) + 40 × 50 100 Ratio of milk to water = 4 = 4 : 1 1
∴ Required answer (i.e. ratio of water to milk) = 1 : 4.
- 15 liters of a mixture contains 20 % alcohol and the rest water. If 3 liters of water be mixed in it, the % of alcohol in the new mixture will be —
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On the basis of given question , we can say that
In the mixture, water is added
Hence, % of water in the mixture = 100 – 20 = 80%
Now applying the given rule, we haveThe percentage of water in the new mixture = 15 z – 80 = 3 100 – z ∴ z = 500 % 6 Required answer i.e. % of alcohol in the new mixture = 100 – 500 = 100 6 6 Correct Option: B
On the basis of given question , we can say that
In the mixture, water is added
Hence, % of water in the mixture = 100 – 20 = 80%
Now applying the given rule, we haveThe percentage of water in the new mixture = 15 z – 80 = 3 100 – z ∴ z = 500 % 6 Required answer i.e. % of alcohol in the new mixture = 100 – 500 = 100 6 6 Required answer = 50 = 16 2 % 3 3
- Fresh fruit contains 72 % water and dry fruits contains 20 % water. How much dry fruit from 100 kg of fresh fruit can be obtained ?
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As per the given question ,
We are concerned with solid part of the fruit (pure portion). Assume Q kg of dry fruit is obtained.
∴ Solid part in fresh fruit = Solid part in dry fruit
⇒ 0·28 × 100 = 0·8 × Q
⇒ Q = 35 kgCorrect Option: D
As per the given question ,
We are concerned with solid part of the fruit (pure portion). Assume Q kg of dry fruit is obtained.
∴ Solid part in fresh fruit = Solid part in dry fruit
⇒ 0·28 × 100 = 0·8 × Q
⇒ Q = 35 kg
∴ 35 kg of dry fruit can be obtained from 100 kg fresh fruit.
