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- Question
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
- Correct Answer
- Rs. 175.50
ExplanationSince 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
Alligation or Mixture problems
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- 1. 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.
- 2. 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 - 3. 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.
- 4. A merchant has 1000 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. 400 kg
- B. 560 kg
- C. 600 kg
- D. 640 kg Discuss
Correct Answer: 600 kg
Explanation:
By the rule of alligation, we have:Profit on 1st part Profit on 2nd part 8% Mean Profit
14%18% 4 6 Ration of 1st and 2nd parts = 4 : 6 = 2 : 3
∴ Quantity of 2nd kind = ❨ 3 x 1000 ❩kg = 600 kg. 5 - 5. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
Options- A. 81 min.
- B. 108 min.
- C. 144 min.
- D. 192 min. Discuss
Correct Answer: 144 min.
Explanation:
Let the slower pipe alone fill the tank in x minutes.Then, faster pipe will fill it in x minutes. 3 ∴ 1 + 3 = 1 x x 36 ⟹ 4 = 1 x 36 ⟹ x = 144 min.
- 6. 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 - 7. 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 - 8. 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.
- 9. 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 - 10. 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.
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