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Alligation or Mixture problems

1. The ratio of water and alcohol in two different containers is 2:3 and 4:5. In what ratio we are required to mix the mixtures of two containers in order to get the new mixture in which the ratio of alcohol and water be 7:5?
Options
A. 7:3
B. 5:3
C. 8:5
D. 2:7

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Correct Answer: 5:3

Explanation:

$W 1 : A 1 W 2 : A 2 . . . . . W N : A N$

2 : 3 4 : 5 5 : 7

$\frac{W 1}{W 1 + A 1} = \frac{2}{5} \frac{W 2}{W 2 + A 2} = \frac{4}{9} \frac{W N}{W N + A N} = \frac{5}{12}$

= 72/180

= 80/180

= 75/180

=> 5 : 3

Therefore, the ratio is 5: 3

2. Ratio of water and milk in a container is 2 : 3. If 40 liter mixture removed from the container and same quantity of milk is added to it then the ratio of water to milk becomes 1 : 4. Find the initial quantity of mixture?
Options
A. 75 lit
B. 80 lit
C. 85 lit
D. 90 lit

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3. A tin a mixture of two liquids A and B in the proportion 4 : 1. If 45 litres of the mixture is replaced by 45 litres of liquid B, then the ratio of the two liquids becomes 2 : 5. How much of the liquid B was there in the tin? What quantity does the tin hold?
Options
A. 58 l
B. 65 l
C. 50 l
D. 62 l

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4. A man pays Rs. 6.40 per litre of milk. He adds water and sells the mixture at Rs. 8 per litre, thereby making 37.5% profit. The proportion of water to milk received by the customers is
Options
A. 1 : 10
B. 10 : 1
C. 9 : 11
D. 11 : 9

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5. A mixture contains 25% milk and rest water. What percent of this mixture must taken out and replaced with milk so that in mixture milk and water may become equal.
Options
A. 31.8%
B. 31%
C. 33.33%
D. 29.85%

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6. In a 40 litre mixture of alcohol & water, the ratio of alcohol and water is 5 : 3. If 20% of this mixture is taken out and the same amount of water is added then what will be the ratio of alcohol and water in final mixture?
Options
A. 1:1
B. 2:1
C. 3:1
D. 1:2

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7. The amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol is?
Options
A. 6 ml
B. 11 ml
C. 15 ml
D. 9 ml

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8. One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.
Options
A. 27 %
B. 26 %
C. 29 %
D. 21 %

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9. An alloy of copper and bronze weight 50g. It contains 80% Copper. How much copper should be added to the alloy so that percentage of copper is increased to 90%?
Options
A. 45 gm
B. 50 gm
C. 55 gm
D. 60 gm

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10. A milkman has 20 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk. If the cost of pure milk is Rs. 18 per litre, then the profit of the milkman, when he sells all the mixture at cost price, the profit %?
Options
A. 22.5%
B. 25%
C. 20%
D. 33.33%

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