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- Question
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%
- Correct Answer
- 20%
ExplanationLet 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
Alligation or Mixture problems
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- 1. 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 - 2. 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
- 3. 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.
- 4. A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
Options- A. 4 litres, 8 litres
- B. 6 litres, 6 litres
- C. 5 litres, 7 litres
- D. 7 litres, 5 litres Discuss
Correct Answer: 6 litres, 6 litres
Explanation:
Let the cost of 1 litre milk be Re. 1Milk in 1 litre mix. in 1st can = 3 litre, C.P. of 1 litre mix. in 1st can Re. 3 4 4 Milk in 1 litre mix. in 2nd can = 1 litre, C.P. of 1 litre mix. in 2nd can Re. 1 2 2 Milk in 1 litre of final mix. = 5 litre, Mean price = Re. 5 8 8 By the rule of alligation, we have:
C.P. of 1 litre mixture in 1st can C.P. of 1 litre mixture in 2nd can 3 4 Mean Price
5 8 1 2 1 8 1 8 ∴ Ratio of two mixtures = 1 : 1 = 1 : 1. 8 8 So, quantity of mixture taken from each can = ❨ 1 x 12 ❩ = 6 litres. 2 - 5. The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:
Options- A. Rs. 18
- B. Rs. 18.50
- C. Rs. 19
- D. Rs. 19.50 Discuss
Correct Answer: Rs. 18
Explanation:
Let the price of the mixed variety be Rs. x per kg.By rule of alligation, we have:
Cost of 1 kg of Type 1 rice Cost of 1 kg of Type 2 rice Rs. 15 Mean Price
Rs. xRs. 20 (20 - x) (x - 15) ∴ (20 - x) = 2 (x - 15) 3 ⟹ 60 - 3x = 2x - 30
⟹ 5x = 90
⟹ x = 18.
- 6. 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.
- 7. 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 Discuss
Correct Answer: 63 kg
Explanation:
S.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 - 8. 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.
- 9. 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 - 10. 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
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