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- Question
How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?
Options- A. 36 kg
- B. 42 kg
- C. 54 kg
- D. 63 kg
- Correct Answer
- 63 kg
ExplanationS.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.∴ C.P. of 1 kg of mixture = Rs. ❨ 100 x 9.24 ❩ = Rs. 8.40 110 By the rule of allilation, we have:
C.P. of 1 kg sugar of 1st kind Cost of 1 kg sugar of 2nd kind Rs. 9 Mean Price
Rs. 8.40Rs. 7 1.40 0.60 ∴ Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27
⟹ x = ❨ 7 x 27 ❩ = 63 kg. 3
Alligation or Mixture problems
Search Results
- 1. Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.
Options- A. 1 : 3
- B. 2 : 3
- C. 3 : 4
- D. 4 : 5 Discuss
Correct Answer: 2 : 3
Explanation:
By the rule of alligation:Cost of 1 kg of 1st kind Cost of 1 kg of 2nd kind 720 p Mean Price
630 p570 p 60 90 ∴ Required ratio = 60 : 90 = 2 : 3.
- 2. A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:
Options- A. 4%
- B. 6¼%
- C. 20%
- D. 25% Discuss
Correct Answer: 20%
Explanation:
Let C.P. of 1 litre milk be Re. 1Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.
C.P. of 1 litre mixture = Re. ❨ 100 x 1 ❩ = 4 125 5 By the rule of alligation, we have:
C.P. of 1 litre of milk C.P. of 1 litre of water Re. 1 Mean Price
Re. 4 5 0 4 5 1 5 ∴ Ratio of milk to water = 4 : 1 = 4 : 1. 5 5 Hence, percentage of water in the mixture = ❨ 1 x 100 ❩% = 20%. 5 - 3. A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
Options- A. 26.34 litres
- B. 27.36 litres
- C. 28 litres
- D. 29.16 litres Discuss
Correct Answer: 29.16 litres
Explanation:
Amount of milk left after 3 operations = [ 40 ❨ 1 - 4 ❩ 3 ] litres 40 = ❨ 40 x 9 x 9 x 9 ❩ = 29.16 litres. 10 10 10 - 4. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
Options- A. Rs. 169.50
- B. Rs. 170
- C. Rs. 175.50
- D. Rs. 180 Discuss
Correct Answer: Rs. 175.50
Explanation:
Since first and second varieties are mixed in equal proportions.So, their average price = Rs. ❨ 126 + 135 ❩ = Rs. 130.50 2 So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
By the rule of alligation, we have:
Cost of 1 kg of 1st kind Cost of 1 kg tea of 2nd kind Rs. 130.50 Mean Price
Rs. 153Rs. x (x - 153) 22.50 ∴ x - 153 = 1 22.50 ⟹ x - 153 = 22.50
⟹ x = 175.50
- 5. In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
Options- A. 3 : 7
- B. 5 : 7
- C. 7 : 3
- D. 7 : 5 Discuss
Correct Answer: 7 : 3
Explanation:
By the rule of alligation:Cost of 1 kg pulses of 1st kind Cost of 1 kg pulses of 2nd kind Rs. 15 Mean Price
Rs. 16.50Rs. 20 3.50 1.50 ∴ Required rate = 3.50 : 1.50 = 7 : 3.
- 6. In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?
Options- A. 3 : 2
- B. 3 : 4
- C. 3 : 5
- D. 4 : 5 Discuss
Correct Answer: 3 : 2
Explanation:
S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10%.C.P. of 1 kg of the mixture = Rs. ❨ 100 x 68.20 ❩ = Rs. 62. 110 By the rule of alligation, we have:
Cost of 1 kg tea of 1st kind. Cost of 1 kg tea of 2nd kind. Rs. 60 Mean Price
Rs. 62Rs. 65 3 2 ∴ Required ratio = 3 : 2.
- 7. A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:
Options- A.
1 3 - B.
2 3 - C.
2 5 - D.
3 5
Discuss
Correct Answer:2 3
Explanation:
By the rule of alligation, we have:Strength of first jar Strength of 2nd jar 40% Mean
Strength
26%19% 7 14 So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2
∴ Required quantity replaced = 2 3 - 8. A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Options- A.
1 3 - B.
1 4 - C.
1 5 - D.
1 7
Discuss
Correct Answer:1 5
Explanation:
Suppose the vessel initially contains 8 litres of liquid.Let x litres of this liquid be replaced with water.
Quantity of water in new mixture = ❨ 3 - 3x + x ❩ litres 8 Quantity of syrup in new mixture = ❨ 5 - 5x ❩ litres 8 ∴ ❨ 3 - 3x + x ❩ = ❨ 5 - 5x ❩ 8 8 ⟹ 5x + 24 = 40 - 5x
⟹ 10x = 16
⟹ x = 8 . 5 So, part of the mixture replaced = ❨ 8 x 1 ❩ = 1 . 5 8 5 - 9. In what ratio must water be mixed with milk to gain 16⅔% on selling the mixture at cost price?
Options- A. 1 : 6
- B. 6 : 1
- C. 2 : 3
- D. 4 : 3 Discuss
Correct Answer: 1 : 6
Explanation:
Let C.P. of 1 litre milk be Re. 1.S.P. of 1 litre of mixture = Re.1, Gain = 50 %. 3 ∴ C.P. of 1 litre of mixture = ❨ 100 x 3 x 1 ❩ = 6 350 7 By the rule of alligation, we have:
C.P. of 1 litre of water C.P. of 1 litre of milk 0 Mean Price
Re. 6 7 Re. 1 1 7 6 7 ∴ Ratio of water and milk = 1 : 6 = 1 : 6. 7 7 - 10. A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
Options- A. 10
- B. 20
- C. 21
- D. 25 Discuss
Correct Answer: 21
Explanation:
Suppose the can initially contains 7x and 5x of mixtures A and B respectively.Quantity of A in mixture left = ❨ 7x - 7 x 9 ❩ litres = ❨ 7x - 21 ❩ litres. 12 4 Quantity of B in mixture left = ❨ 5x - 5 x 9 ❩ litres = ❨ 5x - 15 ❩ litres. 12 4 ∴ ❨ 7x - 21 ❩ 4 = 7 ❨ 5x - 15 ❩ + 9 4 9 ⟹ 28x - 21 = 7 20x + 21 9 ⟹ 252x - 189 = 140x + 147
⟹ 112x = 336
⟹ x = 3.
So, the can contained 21 litres of A.
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