Alligation or Mixture problems
- 1. A container is full of milk. One-third of milk is taken out of it and replaced by same quantity of water. Then again one-third of the mixture is taken out of it and replaced by the same quantity of water. The process is repeated 4 times. If 16 litres of milk is left in the container at the end of 4th operation, find the capacity of the container.
Options- A. 76 litres
- B. 81 litres
- C. 82 litres
- D. 85 litres Discuss
Correct Answer: 81 litres
Explanation:
Let capacity of the container be P liter; then
P(1 ? 1/3)4 = 16
? P (2 / 3)4 = 16
? P(16 / 81) = 16 liters
? P = 81 liters
- 2. The cost of type - I rice is Rs. 15 per kg and type - II is Rs. 20 per kg. If both type - I and type - II are mixed in the ratio of 2 : 3, then find the price per kg of the mixed variety.
Options- A. 19.50
- B. 19
- C. 18.50
- D. 18 Discuss
Correct Answer: 18
Explanation:
Let the price per kg of mixed variety be Rs. P;
then By the rule of alligation,
Now, (20 - P) / (P - 15) = (2 / 3)
? 60 ? 3P = 2P ? 30
? 5P = 90
? P = Rs. 18
- 3. In what ratio of water be mixed with milk to gain 16 2/ 3 % on selling the mixture at cost price?
Options- A. 4 : 3
- B. 2 : 3
- C. 6 : 1
- D. 1 : 6 Discuss
Correct Answer: 1 : 6
Explanation:
Let C.P. of 1 liter milk be Re. 1, Gain = 16 2/3 % = 50/3 %
and S.P. of 1 liter mixture = Re. 1
then C.P. of 1 liter mixture = (1 x (100 x 3) / 350) = Re. (6 / 7)
By the rule of alligation,
Hence, required ratio = (1/ 7) : (6 / 7) = 1 : 6
- 4. 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?
Options- A. 600 ml
- B. 710 ml
- C. 520 ml
- D. None of these Discuss
Correct Answer: None of these
Explanation:
- 5. In a mixture of 60 liters, the ratio of milk and water is 2 : 1. If the ratio of the milk and water is to be 1 : 2, then the amount of water to be further added is ?
Options- A. 20 litres
- B. 30 litres
- C. 40 litres
- D. 60 litres Discuss
Correct Answer: 60 litres
Explanation:
Here , Ratio of milk and water in mixture of 60 litre = 2 : 1
? Quantity of milk = 2y = 40 litre
Quantity of water = y = 20 litre
If ratio of milk and water is to be 1 : 2, then in 40 litres of milk, water should be 80 litre
? Quantity of water to be added = 60 litre.
- 6. A merchant has 50 kg. of sugar part of which he sells at 8 % profit and the rest at 18 % profit. He gains 14 % on the whole. The quantity sold at 18 % profit is ?
Options- A. 20 kg
- B. 30 kg
- C. 15 kg
- D. 35 kg Discuss
Correct Answer: 30 kg
Explanation:
- 7. In what proportion must wheat at Rs. 1·60 per kg be mixed with wheat at Rs. 1·45 per kg. So that the mixture be worth Rs. 1·54 per kg?
Options- A. 2 : 3
- B. 3 : 2
- C. 3 : 4
- D. 4 : 3 Discuss
Correct Answer: 3 : 2
Explanation:
Using the Alligation method ,
Here , C1 = 160 paise , C2 = 145 paise and Mean cost Price ( M ) = 154 paise
Required ratio = ( M - C2 ) : ( C1 - M )
? (Dearer wheat) : (Cheaper wheat) = 9 : 6
Hence , (Dearer wheat) : (Cheaper wheat) = 3 : 2
- 8. The ratio of milk and water in 66 kg of adulterated milk is 5 : 1. Water is added to it to make the ratio 5 : 3. The quantity of water added is ?
Options- A. 22 kg
- B. 24·750 kg
- C. 16·500 kg
- D. 20 kg Discuss
Correct Answer: 22 kg
Explanation:
- 9. Two vessels A and B contains milk and water mixed in the ratio 5 : 3 and 2 : 3. When these mixtures are mixed to form a new mixture containing half milk and half water, they must be taken in the ratio ?
Options- A. 2 : 5
- B. 3 : 5
- C. 4 : 5
- D. 7 : 3 Discuss
Correct Answer: 4 : 5
Explanation:
- 10. In what proportion should water and wine at Rs. 22·50 a liter be mixed to reduce the price to Rs. 18 a liter?
Options- A. 1 : 4
- B. 4 : 1
- C. 2 : 3
- D. 3 : 2 Discuss
Correct Answer: 1 : 4
Explanation:
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