71. A bottle contains two liquids A and B of 420 lit and 180 lit respectively. If 40 litres of mixture is taken out and 20 litre liquid B is poured into the bottle, then find the new ratio of liquid A and Liquid B in the bottle?

एक बोतल में क्रमशः 420 लीटर और 180 लीटर के दो तरल पदार्थ A और B होते हैं। यदि 40 लीटर मिश्रण निकाला जाता है और 20 लीटर तरल B बोतल में डाला जाता है, तो बोतल में तरल A और तरल B का नया अनुपात ज्ञात करें?

A. 17:21
B. 98: 47
C. 42:33
D. 98:41
E. None of these

Option “B” is correct.

The ratio of liquid A and B in bottle = 420: 180 = 7 : 3

40 lit mixture taken out

10x = 40

x= 4

7x = 28 lit liquid A taken out

3x = 12 lit liquid B taken out

Required ratio= (420 – 28) : (180 – 12 +20) = 392: 188 = 98:47

72. A 72 litres solution containing liquids of milk and water in the ratio of 7 : 5 respectively. Find how much amount of milk is to be added in the solution so that the amount of milk is 75% of the newly formed solution?

72 लीटर का घोल जिसमें क्रमशः 7: 5 के अनुपात में दूध और पानी के तरल हैं। ज्ञात कीजिये कि घोल में कितनी मात्रा में दूध डालना है ताकि नवगठित घोल में दूध की मात्रा 75% हो?

A. 52 litre
B. 32 litre
C. 48 litre
D. 36 litre
E. None of these

Option “C” is correct.

Amount of milk in the solution = 72 × 7/12 = 42 litre

Amount of water in the solution = 72 × 5/12 = 30 litre

Let the milk to be added is = x litres

So, milk is to be 75% of new solution, so water is to be 25% of new solution.

So, 25% of new solution = Water in the solution

Then, according to the question,

=> (72 + x) × 25/100 = 30

=> 72 + x = 120

=> x = 48 litre

73. In a vessel, there are two liquids P and Q in the ratio of 5:9, 28 liters of the mixture is taken out and 2 litres of type Q liquid is poured into it, then the new ratio of liquids Q and P thus formed is 2:1, find the initial quantity of mixture in the vessel?

एक बर्तन में, 5: 9 के अनुपात में दो तरल P और Q हैं, मिश्रण के 28 लीटर को बाहर निकाला गया है और 2 लीटर तरल प्रकार Q को उसमें डाला गया है, फिर इस प्रकार गठित तरल Q और P का नया अनुपात 2: 1 है, बर्तन में मिश्रण की प्रारंभिक मात्रा को ज्ञात कीजिये?

A. 44 litres
B. 56 litres
C. 42 litres
D. 70 litres
E. None of these

Option “B” is correct.

Let the initial quantity of liquids P and Q are 5x, 9x

As per above statement,

x=4

Total initial quantity of mixture = 5x+9x = 14*4 =56 litres

74. A vessel contains a mixture of two liquids A and B in the ratio 5: 2. When 4 litres of mixture are drawn off from the vessel and the vessel is filled with liquid B, then the ratio of A and B become 5: 6. How many litres of liquid A was contained by the vessel initially?

एक बर्तन में दो तरल पदार्थ A और B का एक मिश्रण 5:2 के अनुपात में है। जब बर्तन से 4 लीटर मिश्रण बाहर निकाला जाता है और बर्तन को तरल B से भर दिया जाता है, तो A और B का अनुपात 5: 6 हो जाता है। प्रारंभिक बर्तन में कितना लीटर तरल A निहित था?

A. 2 litres
B. 5 litres
C. 1 4/7litres
D. 6 1/4 litres
E. None of these

Option “E” is correct.

Let the initial quantity of liquid A and B be 5x and 2x.

Quantity of A in mixture left = 5x – 5/7 * 4 = 5x – 20/7

Quantity of B in mixture left = 2x – 2/7 * 4 = 2x – 8/7

(5x – 20/7)/ [(2x – 8/7) + 4] = 5/6

=> (35x – 20)/ (14x + 20) = 5/6

=> 6(35x – 20) = 5(14x + 20)

=> 14x = 22 => x = 5 * 11/7 = 7 (6/7) litres

75. Vessel A contains 80 liters mixture of milk and water in the ratio of 3: 2. If x liters of the water is added to the mixture, then the ratio of the water to milk becomes 13: 12. Find the value of x?

बर्तन A में 80 लीटर दूध और पानी का मिश्रण 3: 2 के अनुपात में है। यदि मिश्रण में पानी का x लीटर मिलाया गया है, फिर पानी से दूध का अनुपात 13: 12 हो जाता है। x का मान ज्ञात कीजिए?

A. 10
B. 15
C. 20
D. 25
E. None of these

Option “C” is correct.

Milk in 80 liters = 3/5 * 80 = 48 liters

Water in 80 liters = 2/5 * 80 = 32 liters

48/(32 + x) = 12/13

384 + 12x = 624

12x = 240

x = 20 liters

76. A vessel contains 63 litre mixtures of water and milk in the ratio of 3: 4. If some amount of water is added to the mixture, then the ratio becomes 3: 2, find the quantity of final mixture.

एक बर्तन में 63 लीटर पानी और दूध का मिश्रण 3:4 के अनुपात में है। यदि मिश्रण में कुछ मात्रा में पानी मिलाया जाता है, तो अनुपात 3: 2 हो जाता है, अंतिम मिश्रण की मात्रा ज्ञात कीजिए।

A. 54 litres
B. 36 litres
C. 90 litres
D. 63 litres
E. 81 litres

Option “C” is correct.

Given that

Water = 63/7 * 3 = 27

Milk = 63/7 * 4 = 36

Then

(27 + x)/36 = 3/2

27x + x = 54

x = 27

Required quantity = 63 + 27 = 90

77. 455 ml of a mixture contains milk and water in the ratio of 4: 3. How much more water is to be added to get a new mixture containing milk and water in the ratio of 4: 5?

455 मिलीलीटर के मिश्रण में 4:3 के अनुपात में दूध और पानी है। 4: 5 के अनुपात में दूध और पानी के मिश्रण को प्राप्त करने के लिए कितना अधिक पानी मिलाया जाता है?

A. 210 ml
B. 320 ml
C. 130 ml
D. 520 ml
E. None of these

Option “C” is correct.

Milk = 455 * 4/7 = 65 * 4 = 260 ml

Water = 455 – 260 = 195 ml

Hence we get, 260/(195 + x) = 4/5

=> x = 130 ml

78. A milkman has 75 liters of mixture of milk and water in the ratio of 3:2. In how much water should be added to the mixture, then the ratio of the milk and water becomes 9: 10?

एक दूधवाले के पास 3:2 के अनुपात में 75 लीटर दूध और पानी है। मिश्रण में कितना पानी मिलाया जाना चाहिए, ताकि दूध और पानी का अनुपात 9:10 हो जाए?

A. 10 liters
B. 20 liters
C. 30 liters
D. 15 liters
E. None of these

Option “B” is correct.

Milk = 3 / 5 * 75 = 45

Water = 2/5 * 75 = 30

45 / (30 + x) = 9 / 10

50 = 30 + x

x = 20 liters

79. A milkman has the mixture of milk and water in the ratio of 5: 3 and then he added 20 liters of the water, then the ratio of the milk and water becomes 15: 19. What is the initial quantity of the water in the mixture?

एक दूधवाले के पास दूध और पानी का मिश्रण 5: 3 के अनुपात में है और फिर उसने 20 लीटर पानी मिलाया, फिर दूध और पानी का अनुपात 15:19 हो जाता है। मिश्रण में पानी की प्रारंभिक मात्रा क्या है?

A. 12 liters
B. 15 liters
C. 18 liters
D. 21 liters
E. None of these

Option “C” is correct.

5x/(3x + 20) = 15/19

45x + 300 = 95x

50x = 300

x = 6 liters

Initial quantity of the water = 3 * 6 = 18 liters

80. How many litres of water should be added to a 96 litres mixture containing milk and water in the ratio of 2: 1 such that the resultant mixture is in the ratio of 8: 5?

दूध और पानी वाले 96 लीटर मिश्रण में 2:1 के अनुपात में कितने लीटर पानी मिलाना चाहिए ताकि परिणामी मिश्रण 8:5 के अनुपात में हो?

A. 10 litres
B. 8 litres
C. 12 litres
D. 15 litres
E. None of these

Option “B” is correct.

Total mixture = 96 litres

Milk and water in the ratio of = 2: 1

3’s = 96

1’s = 32

So, Milk = 64 litres, water = 32 litres

Given,

64/(32 + x) = 8/5

32 + x = 40

= > x = 8 litres

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