Alligation or Mixture: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 4)

Let the cheaper price = Rs 25 per kg, the dearer price = Rs 38 per kg, and the mean price = Rs 29 per kg. By alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price) = (38-29) : (29-25) = 9 : 4. Dividing by the HCF 1 gives the simplest ratio 9 : 4. We are told 44 kg of the dearer wheat is used. Let the cheaper quantity be x kg. Then x : 44 = 9 : 4. So x = (9/4) x 44 = 99 kg. Check: 99 kg at Rs 25 plus 44 kg at Rs 38 costs Rs 4147 for 143 kg, which is Rs 29 per kg, matching the mean price of Rs 29.

Let the cheaper price = Rs 17 per kg, the dearer price = Rs 27 per kg, and the mean price = Rs 25 per kg. By alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price) = (27-25) : (25-17) = 2 : 8. Dividing by the HCF 2 gives the simplest ratio 1 : 4. We are told 40 kg of the dearer pulses is used. Let the cheaper quantity be x kg. Then x : 40 = 1 : 4. So x = (1/4) x 40 = 10 kg. Check: 10 kg at Rs 17 plus 40 kg at Rs 27 costs Rs 1250 for 50 kg, which is Rs 25 per kg, matching the mean price of Rs 25.

Let the cheaper price = Rs 21 per kg, the dearer price = Rs 38 per kg, and the mean price = Rs 35 per kg. By alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price) = (38-35) : (35-21) = 3 : 14. Dividing by the HCF 1 gives the simplest ratio 3 : 14. We are told 28 kg of the dearer almonds is used. Let the cheaper quantity be x kg. Then x : 28 = 3 : 14. So x = (3/14) x 28 = 6 kg. Check: 6 kg at Rs 21 plus 28 kg at Rs 38 costs Rs 1190 for 34 kg, which is Rs 35 per kg, matching the mean price of Rs 35.

Let the cheaper price = Rs 27 per kg. Let the dearer price = Rs 57 per kg. Let the mean price of the mixture = Rs 47 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 57 – 47 = 10. Mean price minus cheaper price = 47 – 27 = 20. So the ratio is 10 : 20. Dividing both terms by their HCF 10 gives the simplest ratio 1 : 2. Check: mixing 1 part at Rs 27 with 2 parts at Rs 57 costs Rs 141 for 3 parts. That is Rs 47 per kg, matching the given mean price of Rs 47.

Let the cheaper price = Rs 29 per kg. Let the dearer price = Rs 49 per kg. Let the mean price of the mixture = Rs 44 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 49 – 44 = 5. Mean price minus cheaper price = 44 – 29 = 15. So the ratio is 5 : 15. Dividing both terms by their HCF 5 gives the simplest ratio 1 : 3. Check: mixing 1 part at Rs 29 with 3 parts at Rs 49 costs Rs 176 for 4 parts. That is Rs 44 per kg, matching the given mean price of Rs 44.

Let the cheaper price = Rs 19 per kg. Let the dearer price = Rs 38 per kg. Let the mean price of the mixture = Rs 25 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 38 – 25 = 13. Mean price minus cheaper price = 25 – 19 = 6. So the ratio is 13 : 6. Dividing both terms by their HCF 1 gives the simplest ratio 13 : 6. Check: mixing 13 parts at Rs 19 with 6 parts at Rs 38 costs Rs 475 for 19 parts. That is Rs 25 per kg, matching the given mean price of Rs 25.

Let the cheaper price = Rs 17 per kg. Let the dearer price = Rs 54 per kg. Let the mean price of the mixture = Rs 53 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 54 – 53 = 1. Mean price minus cheaper price = 53 – 17 = 36. So the ratio is 1 : 36. Dividing both terms by their HCF 1 gives the simplest ratio 1 : 36. Check: mixing 1 part at Rs 17 with 36 parts at Rs 54 costs Rs 1961 for 37 parts. That is Rs 53 per kg, matching the given mean price of Rs 53.

Let the cheaper price = Rs 31 per kg. Let the dearer price = Rs 38 per kg. Let the mean price of the mixture = Rs 37 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 38 – 37 = 1. Mean price minus cheaper price = 37 – 31 = 6. So the ratio is 1 : 6. Dividing both terms by their HCF 1 gives the simplest ratio 1 : 6. Check: mixing 1 part at Rs 31 with 6 parts at Rs 38 costs Rs 259 for 7 parts. That is Rs 37 per kg, matching the given mean price of Rs 37.

Let the cheaper price = Rs 8 per kg. Let the dearer price = Rs 40 per kg. Let the mean price of the mixture = Rs 38 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 40 – 38 = 2. Mean price minus cheaper price = 38 – 8 = 30. So the ratio is 2 : 30. Dividing both terms by their HCF 2 gives the simplest ratio 1 : 15. Check: mixing 1 part at Rs 8 with 15 parts at Rs 40 costs Rs 608 for 16 parts. That is Rs 38 per kg, matching the given mean price of Rs 38.

Let the cheaper price = Rs 26 per kg. Let the dearer price = Rs 60 per kg. Let the mean price of the mixture = Rs 28 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 60 – 28 = 32. Mean price minus cheaper price = 28 – 26 = 2. So the ratio is 32 : 2. Dividing both terms by their HCF 2 gives the simplest ratio 16 : 1. Check: mixing 16 parts at Rs 26 with 1 part at Rs 60 costs Rs 476 for 17 parts. That is Rs 28 per kg, matching the given mean price of Rs 28.

Let the cheaper price = Rs 13 per kg. Let the dearer price = Rs 45 per kg. Let the mean price of the mixture = Rs 32 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 45 – 32 = 13. Mean price minus cheaper price = 32 – 13 = 19. So the ratio is 13 : 19. Dividing both terms by their HCF 1 gives the simplest ratio 13 : 19. Check: mixing 13 parts at Rs 13 with 19 parts at Rs 45 costs Rs 1024 for 32 parts. That is Rs 32 per kg, matching the given mean price of Rs 32.

Let the cheaper price = Rs 28 per kg. Let the dearer price = Rs 32 per kg. Let the mean price of the mixture = Rs 31 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 32 – 31 = 1. Mean price minus cheaper price = 31 – 28 = 3. So the ratio is 1 : 3. Dividing both terms by their HCF 1 gives the simplest ratio 1 : 3. Check: mixing 1 part at Rs 28 with 3 parts at Rs 32 costs Rs 124 for 4 parts. That is Rs 31 per kg, matching the given mean price of Rs 31.

Let the cheaper price = Rs 16 per kg. Let the dearer price = Rs 44 per kg. Let the mean price of the mixture = Rs 35 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 44 – 35 = 9. Mean price minus cheaper price = 35 – 16 = 19. So the ratio is 9 : 19. Dividing both terms by their HCF 1 gives the simplest ratio 9 : 19. Check: mixing 9 parts at Rs 16 with 19 parts at Rs 44 costs Rs 980 for 28 parts. That is Rs 35 per kg, matching the given mean price of Rs 35.

Let the cheaper price = Rs 32 per kg. Let the dearer price = Rs 52 per kg. Let the mean price of the mixture = Rs 51 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 52 – 51 = 1. Mean price minus cheaper price = 51 – 32 = 19. So the ratio is 1 : 19. Dividing both terms by their HCF 1 gives the simplest ratio 1 : 19. Check: mixing 1 part at Rs 32 with 19 parts at Rs 52 costs Rs 1020 for 20 parts. That is Rs 51 per kg, matching the given mean price of Rs 51.

Let the cheaper price = Rs 13 per kg. Let the dearer price = Rs 32 per kg. Let the mean price of the mixture = Rs 16 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 32 – 16 = 16. Mean price minus cheaper price = 16 – 13 = 3. So the ratio is 16 : 3. Dividing both terms by their HCF 1 gives the simplest ratio 16 : 3. Check: mixing 16 parts at Rs 13 with 3 parts at Rs 32 costs Rs 304 for 19 parts. That is Rs 16 per kg, matching the given mean price of Rs 16.

Let the cheaper price = Rs 37 per kg. Let the dearer price = Rs 55 per kg. Let the mean price of the mixture = Rs 42 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 55 – 42 = 13. Mean price minus cheaper price = 42 – 37 = 5. So the ratio is 13 : 5. Dividing both terms by their HCF 1 gives the simplest ratio 13 : 5. Check: mixing 13 parts at Rs 37 with 5 parts at Rs 55 costs Rs 756 for 18 parts. That is Rs 42 per kg, matching the given mean price of Rs 42.

Let the cheaper price = Rs 23 per kg. Let the dearer price = Rs 44 per kg. Let the mean price of the mixture = Rs 26 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 44 – 26 = 18. Mean price minus cheaper price = 26 – 23 = 3. So the ratio is 18 : 3. Dividing both terms by their HCF 3 gives the simplest ratio 6 : 1. Check: mixing 6 parts at Rs 23 with 1 part at Rs 44 costs Rs 182 for 7 parts. That is Rs 26 per kg, matching the given mean price of Rs 26.

Let the cheaper price = Rs 34 per kg. Let the dearer price = Rs 55 per kg. Let the mean price of the mixture = Rs 36 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 55 – 36 = 19. Mean price minus cheaper price = 36 – 34 = 2. So the ratio is 19 : 2. Dividing both terms by their HCF 1 gives the simplest ratio 19 : 2. Check: mixing 19 parts at Rs 34 with 2 parts at Rs 55 costs Rs 756 for 21 parts. That is Rs 36 per kg, matching the given mean price of Rs 36.

Let the cheaper price = Rs 36 per kg. Let the dearer price = Rs 67 per kg. Let the mean price of the mixture = Rs 37 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 67 – 37 = 30. Mean price minus cheaper price = 37 – 36 = 1. So the ratio is 30 : 1. Dividing both terms by their HCF 1 gives the simplest ratio 30 : 1. Check: mixing 30 parts at Rs 36 with 1 part at Rs 67 costs Rs 1147 for 31 parts. That is Rs 37 per kg, matching the given mean price of Rs 37.