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All Free Mathematics MCQs with Answers

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1,551 questions · page 48 of 78

941. 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?

  • A. 2
  • B. 8
  • C. 4
  • D. 5
  • E. None of these

Explanation: The original water is 10% of 70 litres, or 7 litres. If x litres of water are added, (7 + x)/(70 + x) = 12.5% = 1/8; hence 8(7 + x) = 70 +…

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Correct answer: 2

942. 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?

  • A. 648
  • B. 888
  • C. 928
  • D. 1184

Explanation: Let the initial quantity in A be x litres. B initially contains 37.5% of x litres = 3x/8, while C contains 5x/8.

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Correct answer: 1184

943. Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?

  • A. Rs. 13.50
  • B. Rs. 14.50
  • C. Rs. 15.50
  • D. Rs. 16.50
  • E. None of these

Explanation: The mixture costs (3 kg x Rs.9 + 7 kg x Rs.15) / 10 kg = Rs.13.20 per kg.

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Correct answer: Rs. 16.50

944. How many liters of oil at Rs.40 per liter should be mixed with 240 liters of a second variety of oil at Rs.60 per liter so as to get a mixture whose cost is Rs.52 per liter?

  • A. 120 liters
  • B. 180 liters
  • C. 110 liters
  • D. 160 liters

Explanation: Let x litres of the Rs.40 per litre oil be added. Equating total cost to the cost of the mixture gives 40x + 240 litres x Rs.60 per litre…

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Correct answer: 160 liters

945. In what ratio should two varieties of sugar of Rs.18 per kg and Rs.24 kg be mixed together to get a mixture whose cost is Rs.20 per kg?

  • A. 1:3
  • B. 3:1
  • C. 1:2
  • D. 2:1Computer Online Quiz

Explanation: Using alligation, the ratio of Rs.18 per kg sugar to Rs.24 per kg sugar is (Rs.24 - Rs.20) : (Rs.20 - Rs.18) = Rs.4 : Rs.2 = 2:1.

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Correct answer: 2:1Computer Online Quiz

946. 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?

  • A. 9:1
  • B. 4:7
  • C. 7:1
  • D. 2:5

Explanation: Initially there are 12 litres of milk and 8 litres of water. Removing 10 litres removes 6 litres of milk and 4 litres of water, leaving 6…

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Correct answer: 9:1

947. A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?

  • A. 7 liters
  • B. 15 liters
  • C. 10 liters
  • D. 9 liters

Explanation: The original 150 litres contains 20% water = 30 litres of water and 120 litres of wine.

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Correct answer: 10 liters

948. In what ratio must water be mixed with milk to gain 16 2/3 % by selling the mixture at cost price?

  • A. 1:6
  • B. 2:3
  • C. 4:3
  • D. 6:1

Explanation: Suppose the mixture contains 6 units of milk and 1 unit of water. Selling 7 units at the cost price of 6 units of milk gives a gain of 1/6…

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Correct answer: 1:6

949. 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%?

  • A. 3:2
  • B. 3:4
  • C. 3:5
  • D. 4:5

Explanation: A selling price of Rs.68.20 per kg at a 10% gain means the mixture's cost price is Rs.68.20 per kg / 1.10 = Rs.62 per kg.

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Correct answer: 3:2

950. 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?

  • A. 72
  • B. 72.9
  • C. 73.8
  • D. 74.7
  • E. None of these

Explanation: Each replacement removes 9 litres from a 90-litre vessel, so 81/90 = 0.9 of the milk remains after each operation.

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Correct answer: 72.9

951. 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_______?

  • A. 16 : 5
  • B. 14 : 5
  • C. 16 : 7
  • D. 19 : 5
  • E. None of these

Explanation: From vessel P, 2 litres contains 2 litres x 62.5% = 1.25 litres of alcohol and 0.75 litres of water.

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Correct answer: 19 : 5

952. Sharjeel has a container which has a mixture of wine and water in it. Wine and water are in the ratio 4:1. Sharjeel spills some of the mixture by accident. He then replaces the spilled amount with water of same quantity. But now the wine to water ratio became 3:2. How much water did Sharjeel add?

  • A. 3/5
  • B. 1/2
  • C. 1/4
  • D. 2/7

Explanation: Take the original mixture as 1 unit, containing 4/5 unit of wine and 1/5 unit of water.

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Correct answer: 1/4

953. 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

  • A. 18 litres
  • B. 24 litres
  • C. 32 litres
  • D. 42 litres

Explanation: Four operations are performed, and each leaves the fraction (V - 8 litres) / V of the wine, where V is the original capacity.

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Correct answer: 24 litres

954. 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:_______?

  • A. Rs. 18
  • B. Rs. 18.50
  • C. Rs. 19
  • D. Rs. 19.50Fun & Trivia

Explanation: For every 5 kg of mixture, there are 2 kg of Type 1 rice and 3 kg of Type 2 rice.

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Correct answer: Rs. 18

955. 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%?

  • A. 3 : 2
  • B. 3 : 4
  • C. 3 : 5
  • D. 4 : 5

Explanation: At a 10% gain, the cost price of the mixture is Rs.68.20 per kg / 1.10 = Rs.62 per kg.

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Correct answer: 3 : 2

956. 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.

  • A. 1 : 3
  • B. 2 : 3
  • C. 3 : 4
  • D. 4 : 5

Explanation: Using alligation, rice at Rs.7.20 per kg : rice at Rs.5.70 per kg = (Rs.6.30 - Rs.5.70) : (Rs.7.20 - Rs.6.30) = Rs.0.60 : Rs.0.90 = 2:3.

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Correct answer: 2 : 3

957. In what proportion must water be added to spirit to gain 20% by selling it at the cost price?

  • A. 2:5
  • B. 1:5
  • C. 3:5
  • D. 4:5

Explanation: If the spirit costs Rs.1 per unit, adding water costing Rs.0 per unit and selling the mixture at Rs.1 per unit gives a 20% gain when water…

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Correct answer: 1:5

958. How much water must be added to a bucket which contains 40 liters of milk at the cost price of Rs.3.50 per liter so that the cost of milk reduces to Rs.2 per liter?

  • A. 25 liters
  • B. 28 litres
  • C. 30 liters
  • D. 35 liters

Explanation: The 40 litres of milk originally cost 40 litres x Rs.3.50 per litre = Rs.140.

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Correct answer: 30 liters

959. Milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively in what ratio the liquids in both the vessels should be mixed to obtain a new mixture in vessel C containing half milk and half water?

  • A. 1:1
  • B. 1:3
  • C. 1:2
  • D. 7:5

Explanation: Vessel A contains 4/7 milk and vessel B contains 2/5 milk. If x litres from A and y litres from B are mixed to obtain half milk, then…

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Correct answer: 7:5

960. Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R?

  • A. Rs.400
  • B. Rs.500
  • C. Rs.300
  • D. Rs.600
  • E. None of these

Explanation: The conditions give P = (Q + R)/2 and Q = (P + R)/3, or Q + R = 2P and P + R = 3Q.

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Correct answer: Rs.500
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