Sail E0 Webinar

Quantitative Aptitude

MIXTURES AND ALLEGATIONS MCQs

Alligations And Mixtures

Total Questions : 245 | Page 4 of 25 pages
Question 31. In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
  1.    80%
  2.    100%
  3.    84%
  4.    87.5%
  5.    None of these
 Discuss Question
Answer: Option E. -> None of these


Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.


Question 32. In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
  1.    40
  2.    44
  3.    48
  4.    52
  5.    None of these
 Discuss Question
Answer: Option B. -> 44


Let the capacity of the can be T litres.Quantity of milk in the mixture before adding milk = 4/9 (T - 8)After adding milk, quantity of milk in the mixture = 6/11 T.6T/11 - 8 = 4/9(T - 8)10T = 792 - 352 => T = 44.


Question 33. A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?
  1.    2
  2.    8
  3.    4
  4.    5
  5.    None of these
 Discuss Question
Answer: Option A. -> 2


Quantity of milk in the mixture = 90/100 (70) = 63 litres.After adding water, milk would form 87 1/2% of the mixture.Hence, if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63 => x = 72Hence 72 - 70 = 2 litres of water must be added.


Question 34. In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
  1.    5 : 6
  2.    3 : 4
  3.    7 : 8
  4.    8 : 9
  5.    None of these
 Discuss Question
Answer: Option A. -> 5 : 6


Let us say the ratio of the quantities of cheaper and dearer varieties = x : yBy the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6


Question 35. All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
  1.    648
  2.    888
  3.    928
  4.    1184
  5.    None of these
 Discuss Question
Answer: Option D. -> 1184


B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.Quantity of water in container C = 8k - 3k = 5kContainer:               A   B    CQuantity of water: 8k  3k   5kIt is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.5k - 148 = 3k + 148 => 2k = 296 => k = 148The initial quantity of water in A = 8k = 8 * 148 = 1184 liters.


Question 36. Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
  1.    16 : 5
  2.    14 : 5
  3.    16 : 7
  4.    19 : 5
  5.    None of these
 Discuss Question
Answer: Option D. -> 19 : 5


Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litresQuantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litresQuantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litresAs 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.


Question 37. A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
  1.    72
  2.    72.9
  3.    73.8
  4.    74.7
  5.    None of these
 Discuss Question
Answer: Option B. -> 72.9


Let the initial quantity of milk in vessel be T litres.Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T For the given problem, T = 90, y = 9 and n = 2.Hence, quantity of  milk finally in the vessel = [(90 - 9)/90]2 (90) =  72.9 litres.


Question 38. The ratio in which the price 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 is:
  1.    1:3
  2.    2:3
  3.    3:4
  4.    4:5
 Discuss Question
Answer: Option A. -> 1:3

(Dearer Rice): (Cheaper Rice) = 60 : 90 = 2:3
 The Ratio In Which The Price At Rs.7.20 A Kg Be Mixed With ...


Question 39. In what ratio must a grocer mix teas 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%?
  1.    3:2
  2.    3:4
  3.    3:5
  4.    4:5
 Discuss Question
Answer: Option A. -> 3:2

S.P of 1kg mix = RS.68.20, Gain = 10%
C.P of 1kg mix =Rs.(100/110 x 68.20) =Rs.62
(Cheaper Tea) : (Dearer Tea) = 3 : 2
 In What Ratio Must A Grocer Mix Teas Worth Rs.60 A Kg And R...


Question 40. In what ratio must water be mixed with milk to gain 16 2/3 % by selling the mixture at cost price?
  1.    1:6
  2.    2:3
  3.    4:3
  4.    6:1
 Discuss Question
Answer: Option A. -> 1:6

Let the C.P of the milk be Re. 1 per litre
Then S.P of 1 litre of mix =Re 1, Gain% =50/3%
C.P of 1 Litre of Mix =Rs(100 x 3/350 x 1) =Re 6/7 In What Ratio Must Water Be Mixed With Milk To Gain 16 2/3 ...
 Ratio of water and milk =1/7 = 6/7 = 1: 6


Latest Videos

Latest Test Papers