Alligation or Mixture problems
- 1. An alloy contains gold and silver in the ratio 5 : 8 and another alloy contains gold and silver in the ratio 5 : 3. If equal amount of both the alloys are melted together, then the ratio of gold and silver in the resulting alloy is?
Options- A. 113/108
- B. 105/103
- C. 108/115
- D. 103/113 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 105/103
Explanation:
As given equal amounts of alloys are melted, let it be 1 kg.
Required ratio of gold and silver =
Hence, ratio of gold and silver in the resulting alloy = 105/103.
- 2. In a 100 litre of mixture the ratio of milk and water is 6:4. How much milk must be added to the mixture in order to make the ratio 3 : 1?
Options- A. 85
- B. 60
- C. 55
- D. 45 Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 60
Explanation:
Let M litres milk be added
=>
=> 60 + M = 120
=> M = 60 lit.
- 3. If a man buys 1 lt of milk for Rs.12 and mixes it with 20% water and sells it for Rs.15, then what is the percentage of gain?
Options- A. 25%
- B. 30%
- C. 17%
- D. 19% Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 25%
Explanation:
He has gain = 15 - 12 = 3,
Gain% = (3/12) x 100 = (100/4) = 25.
He has 25% gain.
- 4. Manideep purchases 30kg of barley at the rate of 11.50/kg and 20kg at the rate of 14.25/kg. He mixed the two and sold the mixture in the shop. At what price per kg should he sell the mixture to make 30% profit to him?
Options- A. 15.84
- B. 14.92
- C. 13.98
- D. 16.38 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 16.38
Explanation:
Given, Manideep purchases 30kg of barley at the rate of 11.50/kg nad 20kg at the rate of 14.25/kg.
Total cost of the mixture of barley = (30 x 11.50) + (20 x 14.25)
=> Total cost of the mixture = Rs. 630
Total kgs of the mixture = 30 + 20 = 50kg
Cost of mixture/kg = 630/50 = 12.6/kg
To make 30% of profit
=> Selling price for manideep = 12.6 + 30% x 12.6
=> Selling price for manideep = 12.6 + 3.78 = 16.38/kg.
- 5. Shiva purchased 280 kg of Rice at the rate of 15.60/kg and mixed it with 120 kg of rice purchased at the rate of 14.40/kg. He wants to earn a profit of Rs. 10.45 per kg by selling it. What should be the selling price of the mix per kg?
Options- A. Rs. 22.18
- B. Rs. 25.69
- C. Rs. 26.94
- D. Rs. 27.54 Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: Rs. 25.69
Explanation:
Rate of rice of quantity 280 kg = Rs. 15.60/kg
Rate of rice of quantity 120 kg = Rs. 14.40/kg
He want to earn a profit of Rs. 10.45/kg
Rate of Mix to sell to get profit of 10.45 =
- 6. Two bottles contains mixture of milk and water. First bottle contains 64% milk and second bottle contains 26% water. In what ratio these two mixtures are mixed so that new mixture contains 68% milk?
Options- A. 3 : 2
- B. 2 : 1
- C. 1 : 2
- D. 2 : 3 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 3 : 2
Explanation:
% of milk in first bottle = 64%
% of milk in second bottle = 100 - 26 = 74%
Now, ATQ
64% 74%
68%
6 4
Hence, by using allegation method,
Required ratio = 3 : 2
- 7. 640 ml of a mixture contains milk and water in ratio 6:2. How much of the water is to be added to get a new mixture containing half milk and half water?
Options- A. 360 ml
- B. 320 ml
- C. 310 ml
- D. 330 ml Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 320 ml
Explanation:
Here total parts of milk and water in the solution is 6+2 = 8 parts.
1part = 640/8 = 80
old mixture contains 6parts of milk and 2 parts of water(6:2).
To get new mixture containing half milk and half water, add 4parts of water to the old mixture then 6:(2+4) to make the ratio same.
i.e, 4 x 80 = 320 ml.
- 8. A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Options- A. 5 lit
- B. 10 lit
- C. 15 lit
- D. 20 lit Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 10 lit
Explanation:
Number of liters of water in 150 liters of the mixture = 20% of 150 = 20/100 x 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 x (150 + P)
120 + 4P = 150 + P => P = 10 liters.
- 9. In a mixture, the ratio of juice and water is 4 : 3. By adding 6 litre water the ratio of juice and water will be 8 : 7. What is the amount of juice in the original mixture?
Options- A. 38 lit
- B. 96 lit
- C. 48 lit
- D. 52 lit Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 48 lit
Explanation:
Let the amount of juice and water in original mixture '4x' litre and '3x' litre respectively.
According to given data,
4x/3x+6 =8/7
28x=24x+48
28x?24x=48
4x = 48
x = 12
Amount of juice = 4x = 4×12 = 48 litre.
- 10. From container A containing 54 liter of mixture of milk and water in ratio of 8 : 1 , 18 liter of the mixture is taken out and poured into container B in which ratio of milk to water is 3 : 1. If difference between total milk and total water in container B is 30 liter then find the quantity of initial mixture in container B.
Options- A. 30 Liter
- B. 28 Liter
- C. 32 Liter
- D. 36 Liter Also asked in: AIEEE, Bank Exams, CAT
Correct Answer: 32 Liter
Explanation:
Let initially milk and water in container B is 3x liter and x liter respectively
Now, 3x + (8/9) × 18 ? x ? (1/9) × 18 = 30
3x + 16 ? x ? 2 = 30
x = 8
Initial quantity is container B = 8 (3 + 1) = 32 Liter.
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