alligation-or-mixture gate question and answers -Page 4

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Alligation or Mixture problems

1. In a pot, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk, the pot would be full and ratio of milk and water would become 6 : 5. Find the capacity of the pot ?
Options
A. 11 lit
B. 22 lit
C. 33 lit
D. 44 lit

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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 vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained ?
Options
A. 5:3
B. 1:4
C. 4:1
D. 9:1

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4. From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus, in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the container was:
Options
A. 75 litres
B. 100 litres
C. 150 litres
D. 120 litres

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Correct Answer: 120 litres

Explanation:

$\frac{w i n e (l e f t)}{w i n e (a d d e d)} = \frac{343}{169}$

It means $\frac{w i n e (l e f t)}{w i n e (i n i t i a l a m o u n t)} = \frac{343}{512}$ (since 343 + 169 = 512)

Thus, $343 x = 512 x {(1 - \frac{15}{k})}^{3}$

$\frac{343}{512} = {(\frac{7}{8})}^{3} = {(1 - \frac{15}{k})}^{3}$

$(1 - \frac{15}{k}) = \frac{7}{8} = (1 - \frac{1}{8})$

Thus the initial amount of wine was 120 liters.

5. 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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6. In a mixture of milk and water the proportion of water by weight was 75%. If in 60 gm of mixture 15 gm water was added, what would be the percentage of water ? (Weight in gm)
Options
A. 80%
B. 70%
C. 75%
D. 62%

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7. In a 48 ltr mixture, the ratio of milk and water is 5:3. How much water should be added in the mixture so as the ratio will become 3:5 ?
Options
A. 24 lit
B. 16 lit
C. 32 lit
D. 8 lit

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8. 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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9. A milkman claims to sell milk at its cost price, still, he is making a profit of 30% since he has mixed some amount of water in the milk. What is the % of milk in the mixture?
Options
A. 71.02%
B. 76.92%
C. 63.22%
D. 86.42%

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10. 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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