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Quantitative Aptitude

MIXTURES AND ALLEGATIONS MCQs

Alligations And Mixtures

Total Questions : 245 | Page 17 of 25 pages
Question 161. Rs. 675 was divided among 75 boys and girls. Each boy gets Rs. 20 whereas a girl gets Rs. 5. Find the number of boys and girls.
  1.    15 , 60
  2.    20 , 55
  3.    30 , 45
  4.    25 , 50
 Discuss Question
Answer: Option B. -> 20 , 55

Average money per head (boy or girl) = Rs. (675 / 75) = Rs. 9
Number of boys = 4 / (4 + 11) × 75 = 20
Number of girls = 11 / (4 + 11) × 75 = 55.


Question 162. A cask full of wine from which 8 litres are drawn and is then filled with water. This operation is performed three more times. The ratio of quantity of wine left in the cask to that of the water is 16: 81. How much wine did the cask hold originally?
  1.    24 litres
  2.    42 litres
  3.    32 litres
  4.    18 litres
 Discuss Question
Answer: Option A. -> 24 litres

Let A liters wine cask hold originally, then A[1 - (8 / A)]4 / A = 16 / 81 ? (1 - (8 / A))4 = (2 / 3 )4 ? (1 - (8 / A)) = (2 / 3) ? (8 / A) = (1 - (2 /3)) ? (8 / A) = (1 / 3)? A = 24 liters


Question 163. A sum of Rs. 41 was divided among 50 boys and girls. Each boy gets 90 paise and a girl 65 paise. The number of boys is ?
  1.    36
  2.    34
  3.    14
  4.    16
 Discuss Question
Answer: Option B. -> 34

Average money per head (boy or girl) = Rs. (675 / 75) = Rs. 9
Number of boys = 4 / (4 + 11) × 75 = 20
Number of girls = 11 / (4 + 11) × 75 = 55.


Question 164. Some amount out of Rs. 7000 was lent at 6 % p.a. and the remaining at 4 % p. a. If the total simple interest from both the fractions in 5 years was Rs. 1600, the sum lent at 6 % p. a. was ?
  1.    None of these
  2.    Rs. 2000
  3.    Rs. 5000
  4.    Rs. 3500
 Discuss Question
Answer: Option B. -> Rs. 2000
Question 165. Sugar at Rs. 15 per kg is mixed with sugar at Rs. 20 per kg in the ratio 2 : 3. Find the price per kg of the mixture?
  1.    Rs. 19
  2.    Rs. 17
  3.    Rs. 18
  4.    Rs. 16
 Discuss Question
Answer: Option C. -> Rs. 18
Question 166. 15 liters of a mixture contains 20 % alcohol and the rest water. If 3 liters of water be mixed in it, the % of alcohol in the new mixture will be ?
  1.    18 1 2
  2.    16 2 3
  3.    15
  4.    17
 Discuss Question
Answer: Option B. -> 16 2 3

According to question , Total C. P. of 200 kg of mixture = Rs. (80 × 6·75 + 120 × 8)Total C. P. of 200 kg of mixture = Rs. 1500Average rate = Rs. 7·50 per kgRequired rate = 120% of Rs. 7·50Required rate = Rs. 9 per kg.


Question 167. A grocer buys two kind of rice at Rs. 1·80 and Rs. 1·20 per kg respectively. In what proportion should these be mixed, so that by selling the mixture at Rs. 1·75 per kg, 25 % may be gained?
  1.    2 : 1
  2.    3 : 4
  3.    3 : 2
  4.    1 : 2
 Discuss Question
Answer: Option D. -> 1 : 2

According to question , Total C. P. of 200 kg of mixture = Rs. (80 × 6·75 + 120 × 8)Total C. P. of 200 kg of mixture = Rs. 1500Average rate = Rs. 7·50 per kgRequired rate = 120% of Rs. 7·50Required rate = Rs. 9 per kg.


Question 168. Kantilal mixes 80 kg of sugar worth of Rs. 6·75 per kg with 120 kg worth of Rs. 8 per kg. At what rate shall he sell the mixture to gain 20 %?
  1.    Rs. 9
  2.    Rs. 8·20
  3.    Rs. 8·85
  4.    Rs. 7·50
 Discuss Question
Answer: Option A. -> Rs. 9

According to question , Total C. P. of 200 kg of mixture = Rs. (80 × 6·75 + 120 × 8)Total C. P. of 200 kg of mixture = Rs. 1500Average rate = Rs. 7·50 per kgRequired rate = 120% of Rs. 7·50Required rate = Rs. 9 per kg.


Question 169. A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
  1.    5:3
  2.    4:1
  3.    9:1
  4.    1:4
 Discuss Question
Answer: Option C. -> 9:1

According to question,Quantity of Milk/Quantity of Water = 3/2Let us assume the product ratio = n.Quantity of Milk = 3n and Quantity of Water = 2n litersQuantity of Milk + Quantity of Water = 20 liters3n + 2n = 20 liters5n = 20 litersn = 20/5n = 4Quantity of Milk = 3n litersPut the value of n,Quantity of Milk = 3 x 4 = 12 litersQuantity of Water = 2n Quantity of Water = 2 x 4 = 8 litersIf 10 liters of mixture are removed first time, we will find how much milk and water contain in mixture.? 20 liters of mixture contains 12 liter of milk.? 1 liters of mixture contains 12/20 liter of milk.? 10 liters of mixture contains 10 x 12/20 liter of milk.? 10 liters of mixture contains 6 liter of milk.? 10 liters of mixture contains 4 liter of water.If 10 liters of mixture are removed, then amount of milk removed = 6 liters and amount of water removed = 4 liters. Remaining milk = 12 - 6 = 6 litersRemaining water = 8 - 4 = 4 liters10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters and water = 4 liters.If the process is repeated one more time and 10 liters of the mixture are removed second time, thenIf 10 liters of mixture are removed, Again we will find how much milk and water contain in the mixture.? 20 liters of mixture contains 16 liter of milk.? 1 liters of mixture contains 16/20 liter of milk.? 10 liters of mixture contains 10 x 16/20 liter of milk.? 10 liters of mixture contains 8 liter of milk.? 10 liters of mixture contains 2 liter of water.If 10 liters of mixture are removed, then amount of milk removed = 8 liters and amount of water removed = 2 liters.Remaining milk = (16 - 8) = 8 liters.Remaining water = (4 - 2) = 2 liters.Now 10 liters milk is added => total milk = 18 liters and water will be 2 liters.The required ratio of milk and water in the final mixture obtainedQuantity of milk/Quantity of Water= 18:2 = 9:1


Question 170. In what ratio must a grocer mix sugar at 72 paise per kg with sugar at 48 paise per kg. So that by selling the mixture at 63 paise per kg he may gain 1 of his out-lay? 6
  1.    1 : 3
  2.    3 : 1
  3.    3 : 2
  4.    2 : 3
 Discuss Question
Answer: Option A. -> 1 : 3

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