Alligation or Mixture
- 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.
- 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 ,
- Two casks of 48 and 42 liters are filled with mixture of wine and water13 : 7 and 18 : 17. If the contents of the two casks be mixed and 20 liters of water added to the whole what will be the proportion of wine to water in the result?
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Ratio of wine to water, when 20 litre of water are not added
= 
13 × 48 + 18 × 42 
: 7 × 48 + 17 × 42 20 35 20 35
Ratio of wine to water, when 20 litre of water are not added = 264 : 186 = 44 : 31
Now, 20 litres of water are added .Quantity of wine = 48 + 42 × 44 44 + 31 Quantity of wine = 264 litres 5 and Quantity of water = 20 + 48 + 42 × 31 44 + 31 Quantity of water = 186 + 20 5 Quantity of water = 286 5
Correct Option: B
Ratio of wine to water, when 20 litre of water are not added
= 13 × 48 + 18 × 42 : 7 × 48 + 17 × 42 20 35 20 35
Ratio of wine to water, when 20 litre of water are not added = 264 : 186 = 44 : 31
Now, 20 litres of water are added .Quantity of wine = 48 + 42 × 44 44 + 31 Quantity of wine = 264 litres 5 and Quantity of water = 20 + 48 + 42 × 31 44 + 31 Quantity of water = 186 + 20 5 Quantity of water = 286 5 ∴ Required ratio = 264 : 286 5 5
Thus , Required ratio = 12 : 13
- Currants at Rs. 50 per kg are mixed with currants at Rs. 90 per kg to make a mixture of 17 kg worth Rs. 70 per kg. How many kilograms of each are taken ?
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Here , C1 = Rs . 90 , C2 = Rs . 50 and Mean cost Price ( M ) = Rs . 70
As we know that ,Required ratio = 90 – 70 = 1 : 1 70 – 50 Correct Option: B
Here , C1 = Rs . 90 , C2 = Rs . 50 and Mean cost Price ( M ) = Rs . 70
As we know that ,Required ratio = 90 – 70 = 1 : 1 70 – 50 Hence, 17 = 8 1 kg of each are taken . 1 + 1 2
- 729 ml of a mixture 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 ratio 7 : 3 ?
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Given :- Quantity of Mixture = 729 ml and Ratio of milk and water = 7 : 2
According to question ,Percentage of water in first mixture = 2 × 100 2 + 7 Percentage of water in first mixture = 200 % 9 Percentage of water in the second mixture = 3 × 100 = 30% 7 + 3
Now, applying the given rule,
Correct Option: D
Given :- Quantity of Mixture = 729 ml and Ratio of milk and water = 7 : 2
According to question ,Percentage of water in first mixture = 2 × 100 2 + 7 Percentage of water in first mixture = 200 % 9 Percentage of water in the second mixture = 3 × 100 = 30% 7 + 3
Now, applying the given rule,Required answer = 30 - 200/9 × 729 100 - 30
Required answer = 81 ml.
