Mixture and Alligation 2
In 1 kg mixture of sand and iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10%?
In 1 kg mixture quantity of iron = 200 gm
Let x gm sand should be added, then
10% of (1000 + x) = 200
∴ x = 1000 gm = 1 kg
In a mixture of milk and water the proportion of water by weight was 75%. If in the 60 gms mixture 15 gm. water was added, what would be the percentage of water? (weight in gms.)
In 60 gms mixture proportion of water
=
= 45 gms
Total proportion of water in new mixture
= 45 + 15 = 60 gms.
∴ Percentage of water
= 80%
Jaydeep purchased 25 kg of rice at the rate of ₹16.50 per kg and 35 kg of rice at the rate of ₹24.50 per kg. He mixed the two and sold the mixture. Approximately, at what price per kg did he sell the mixture to make 25 per cent profit?
CP = 25 × 16.50 + 35 × 24.50 = ₹1270
SP = 1270 ×
Price per kg
How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay?
Here, cost price of mixture
∴
and hence
The number of millilitres of water added to reduce 9 ml of aftershave lotion, containing 50% alcohol, to a lotion containing 30% alcohol is
The given solution has 50% alcohol. Water which is to be added has 0% alcohol concentration.
Alcohol concentration :
∴ Water should be added in the ratio 2 : 3
∴ Quantity of water to be added
An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again, it was filled with B type of petrol. At this time, what was the percentage of A type of petrol in the tank?
Now, amount of petrol A
∴ required % × l00
= 37.50%
Five litres of water is added to a certain quantity of pure milk costing ₹3 per litre. If by selling the mixture at the same price as before, a profit of 20% is made, what is the amount of pure milk in the mixture?
Here, S. P. of mixture = C. P. of pure milk = ₹3 per litre
Now, S. P. of mixture
Also, C. P of water = ₹0
By the rule of alligation :
∴ Ratio of pure milk and water in mixture
For five litres of water, quantity of pure milk
= 5 × 5 = 25 litres
Three bars of gold, weighing 6, 5, 4 and of 15, 14, 12½ carats fineness are mixed together. What is the fineness of the compound?
How many kilograms of tea powder costing ₹31 per kg be mixed with thirty six kilograms of tea powder costing ₹43 per kg, such that the mixture when sold at ₹44 per kg gives profit of 10%?
C.P. of the mixture
= ₹40 per kg
Using alligation rule, the required ratio
= 1 : 3
If 3 → 36 kg, then 1 → ?
= = 12 kg.
A trader mixes 80 kg of tea at ₹15 per kg with 20 kg of tea at cost price of ₹20 per kg. In order to earn a profit of 25%, what should be the sale price of the mixed tea?
C.P. of mixture
∴ S.P.
A company blends two varieties of tea from two different tea gardens, one variety costing ₹20 per kg and other ₹25 per kg, in the ratio 5 : 4. He sells the blended tea at ₹23 per kg. Find his profit percent:
Let the quantity of two varieties of tea be 5x kg and 4x kg, respectively.
Now, SP = 23 × 9x = 207x
and CP = 20 × 5x + 25 × 4x = 200x
Profit % =
In what ratio must water be mixed with milk to gain 20% by selling the mixture at cost price?
Let C.P. of milk be Re. 1 per litre.
Then, S.P. of 1 litre of mixture = Re. 1.
Gain = 20%
∴ C.P. of 1 litre of mixture
= ₹
By the rule of alligation, we have :
∴ Ratio of water and milk
Two liquids are mixed in the proportion of 3 : 2 and the mixture is sold at ₹11 per kg at a 10% profit. If the first liquid costs ₹2 more per kg than the second, what does it cost per litre?
Let the cost of second liquid be ₹x.
Then, cost of first liquid be ₹(x + 2).
⇒ 5x + 6 = 50 ⇒ x = ₹8.8
∴ cost of first liquid
= ₹(8.8 + 2) = ₹10.80
In what ratio must water be mixed with milk to gain 16⅔% on selling the mixture at cost price?
Let C.P. of 1 litre milk be Re. 1.
S.P. of 1 litre of mixture
= Re. 1, Gain = 50/3%
∴ C.P. of 1 litre of mixture = Re 6/7.
= = 1 : 6.
A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:
So, ratio of 1st and 2nd quantities
= 7 : 14 = 1 : 2.
∴ Required quantity replaced = ⅔
How many litres of pure alcohol must be added to 10 litres of mixture which is 15% alcohol to make a mixture which will be 25% alcohol?
By the rule of alligation, Alcohol concentration :
∴ Alcohol must be added in the ratio of 10 : 75 or 2 : 15
∴ Quantity of alcohol to be added in 10 litres
How many kg of custard powder costing ₹40 kg must be mixed with 16 kg of custard powder costing ₹55 kg so that 25% may be gained by selling the mixture at ₹60 kg?
C. P. of mixture
Let x kg be mixed. Then,
A butler stole wine from a butt of sherry which contained 32% of spirit and then replaced what he stole, by wine containing only 18% spirit. The butt was then of 24% strength only. How much of the butt had he stolen?
By the rule of alligation,
Now, wine of 32% spirit
∴ The rest part
i.e of the butt has been stolen.
A chemist has 10 litres of a solution that is 10 per cent nitric acid by volume. He wants to dilute the solution to 4 per cent strength by adding water. How many litres of water must he add?
10% of 10 litre is 1 litre.
1 ltr. is 4% of 25 litre. So final solution will have
Hence 15 litres of water needs to be added.
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