Alligation or Mixture problems
- 1. In what ratio must wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg so that the mixture be worth Rs. 3/kg?
Options- A. 1:2
- B. 3:2
- C. 2:1
- D. 2:3 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 2:1
Explanation:
Given rate of wheat at cheap = Rs. 2.90/kg
Rate of wheat at cost = Rs. 3.20/kg
Mixture rate = Rs. 3/kg
Ratio of mixture =
2.90 3.20
3
(3.20 - 3 = 0.20) (3 - 2.90 = 0.10)
0.20 : 0.10 = 2:1
Hence, wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg in the ratio of 2:1, so that the mixture be worth Rs. 3/kg.
- 2. 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.
- 3. 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.
- 4. 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.
- 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. 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 Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 5:3
- 8. 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 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 80 lit
Explanation:
From the given data,
let the initial quantity of the mixture = 5x
Then,
Then the initial quantity of the mixture = 5x = 5 x 16 = 80 lit.
- 9. 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 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 50 l
Explanation:
Let the tin contain 5x litres of liquids
=> 5(4x - 36) = 2(x + 36)
=> 20x - 180 = 2x + 72
=> x = 14 litres
Hence, the initial quantity of mixture = 70l
Quantity of liquid B
=
= 50 litres.
- 10. 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 Also asked in: CAT, GATE, Analyst, Bank Clerk, Bank PO, AIEEE, Bank Exams
Correct Answer: 1 : 10
Explanation:
Customer ratio of Milk and Water is given by
Milk :: Water
6.4 0
=> Milk : Water = 110 : 11 = 10 : 1
Therefore, the proportionate of Water to Milk for Customer is 1 : 10
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