21. Two glasses A and B of quantity 200 ml contains milk-water mixture in the ratio 3 ∶ 2 and 3 ∶ 7 respectively. From glass A, 50 ml of the mixture is removed and replaced with water. From glass B, 100 ml of mixture is removed and replaced with milk. If the mixture of the two glasses is mixed, what is the ratio of milk and water in the final mixture?

200 मिलीलीटर की मात्रा वाले दो गिलास A और B में क्रमशः 3 ∶ 2 और 3 : 7 के अनुपात में दूध-पानी का मिश्रण है। गिलास A से, मिश्रण के 50 मिलीलीटर को निकाला जाता है और पानी से बदल दिया जाता है। गिलास B से, मिश्रण के 100 मिलीलीटर को निकाला जाता है और दूध से बदल दिया जाता है। यदि दो गिलासों का मिश्रण मिश्रित किया जाता है, तो अंतिम मिश्रण में दूध और पानी का अनुपात क्या है?

Option “D” is correct.

Considering glass A,

Initial ratio of milk-water mixture = 3 ∶ 2

∵ 50 ml of mixture is removed and replaced with water

⇒ Quantity of milk in glass A = 3/5 × (200 – 50) = 3/5 × 150 = 90 ml

⇒ Quantity of water in glass A = [2/5 × (200 – 50)] + 50 = (2/5 × 150) + 50 = 60 + 50 = 110 ml

Considering glass B,

Initial ratio of milk-water mixture = 3 ∶ 7

∵ 100 ml of mixture is removed and replaced with milk

⇒ Quantity of milk in glass B = [3/10 × (200 – 100)] + 100 = (3/10 × 100) + 100 = 30 + 100 = 130 ml

⇒ Quantity of water in glass B = 7/10 × (200 – 100) = 7/10 × 100 = 70 ml

Now, if the mixtures of the two glasses are mixed,

⇒ Quantity of milk in final mixture = 90 + 130 = 220 ml

⇒ Quantity of water in final mixture = 110 + 70 = 180 ml

∴ Ratio of milk and water in final mixture = 220 ∶ 180 = 11 ∶ 9

22. In 60L mixture of milk and water; the ratio of milk and water is 2:3. How much water should be added in the mixture so that the ratio of milk and water becomes 1:4?

दूध और पानी के 60 लीटर मिश्रण में, दूध और पानी का अनुपात 2: 3 है। मिश्रण में कितना पानी मिलाया जाना चाहिए ताकि दूध और पानी का अनुपात 1: 4 हो जाएगा?

Option “A” is correct.

Quantity of milk = 60 × (2/5) = 24L

Quantity of water = 60 × (3/5) = 36L

now after adding x litre of water to it

24/(36 + x) = 1/4

96 = 36 + x 

∴ x = 60L 

23. A and B are two mixture which are prepared by mixing alcohol, beer and water in the ratio of 2 ∶ 3 ∶ 4 and 3 ∶ 4 ∶ 5 respectively. If equal quantities of mixture are mixed to form a third mixture C then what is the ratio of alcohol, beer and water in mixture C?

A और B दो प्रकार के मिश्रण हैं जिन्हें एल्कोहल, बीयर और पानी को क्रमशः 2 ∶ 3 ∶ 4 और 3 ∶ 4 ∶ 5 के अनुपात में मिला कर तैयार किया जाता है। यदि मिश्रणों की समान मात्राओं को तीसरा मिश्रण C बनाने के लिए मिलाया जाता है, तब मिश्रण C में एल्कोहल, बीयर और पानी का अनुपात क्या होगा?

Option “C” is correct.

Ratio of alcohol, beer and water in mixtre A = 2 ∶ 3 ∶ 4 = 9 units

Ratio of alcohol, beer and water in mixtre B = 3 ∶ 4 ∶ 5 = 12 units

We have to euqal quantities

Ratio of alcohol, beer and water in mixtre A = 2 ∶ 3 ∶ 4 = 9 units × 4

Ratio of alcohol, beer and water in mixtre B = 3 ∶ 4 ∶ 5 = 12 units × 3

New ratio of alcohol, beer and water in mixtre A = 8 ∶ 12 ∶ 16 = 36 unit

New ratio of alcohol, beer and water in mixtre B = 9 ∶ 12 ∶ 15 = 36 unit

So, ratio of alcohol, beer and water in mixtre C = (8 + 9) ∶ (12 + 12) ∶ (16 + 15) = 17 ∶ 24 ∶ 31

24. The ratio (by volume) of milk and water in a mixture is 2 : 1. If we add 12 litres of water in the mixture, then the ratio of milk and water becomes 4 :3. What is the quantity of water in the new mixture?

एक मिश्रण में दूध और पानी का अनुपात (आयतन से) 2 : 1 है। यदि हम मिश्रण में 12 लीटर पानी मिलाते हैं, तो दूध और पानी का अनुपात 4 : 3 हो जाता है। तो नए मिश्रण में पानी की मात्रा क्या है?

Option “A” is correct.

Let the quantity of milk and water in the mixture are 2x and x respectively

After adding water in the mixture, the quantity of water in the mixture will be (x + 12)

According to question,

2x/(x + 12) = 4/3

⇒ 6x = 4(x + 12)

⇒ 6x = 4x + 48

⇒ 2x = 48

⇒ x = 24

So, the quantity of water in the new mixture = 24 + 12 = 36

∴ The quantity of water in the new mixture will be 36 litres.

25. The ratio of milk and water in a mixture is 4 : 3. If we add 2 litres of water, the ratio of milk and water becomes 8 : 7. What is the quantity of the final mixture?

एक मिश्रण में दूध और पानी का अनुपात 4 : 3 है। यदि हम मिश्रण में 2 लीटर पानी मिलाते हैं, तो दूध और पानी का अनुपात 8 : 7 हो जाता है। तो अंतिम मिश्रण की मात्रा क्या है?

Option “B” is correct.

Ratio of milk and water in a mixture is = 4x : 3x

According to the question

4x/(3x + 2) = 8/7

⇒ 4x × 7 = 8 (3x + 2)

⇒ 28x = 24x + 16

⇒ 28x – 24x = 16

⇒ 4x = 16

⇒ x = 16/4

⇒ x = 4

Quantity of mixture in the last = (4x + 3x) = 7x = 7 × 4 = 28 litres

Quantity of mixture in the last = 28 + 2 = 30 litres

26. A mixture contains milk and water in the ratio 5 : 3. If 5 litres of milk is added to the mixture, the ratio becomes 7 : 3. What is the quantity of milk in the new mixture?

एक मिश्रण में दूध और पानी का अनुपात 5 : 3 है। यदि मिश्रण में 5 लीटर दूध मिलाया जाता है, तो अनुपात 7 : 3 हो जाता है। नए मिश्रण में दूध की मात्रा क्या है?

Option “C” is correct.

Let the quantity of milk and water be 5x and 3x.

According to question,

⇒ {(5x + 5)/(8x + 5)} = 7/10

⇒ 50x + 50 = 56x + 35

⇒ 6x = 15

⇒ x = 2.5 litre

⇒ New quantity of milk = 7x = 7 × 2.5 = 17.5 litres

∴ The new quantity of milk is 17.5 litres.

27.100 Liters of mixture contains 15% water and rest milk, the amount of milk that must be added so that the resulting mixture contains 87.5% milk is?

100 लीटर मिश्रण में 15% पानी और शेष दूध है, इसमें दूध की कितनी मात्रा मिलायी जानी चाहिए ताकि परिणामी मिश्रण में 87.5% दूध हो?

Option “A” is correct.

Amount of water in the mixture = 15% of 100 liters 

⇒ 15 liters

Amount of milk in the mixture = (100 – 15) liters  

⇒ 85 liters

On adding the milk to make the concentration of milk 87.5%,

i.e The quantity of the water remains the same,

⇒ 12.5% Water = 15 liters

⇒ 100% = 120 litersL

⇒ Out of 120 liters, concentration of water is 15 liters

⇒ Quantity of milk = 105 liters

∴ Quantity added = 105 – 85 = 20 liters

28. Two alloys A and B contain copper and zinc in the ratio 7 : 2 and 5 : 3 respectively. How many kg of A and B must be melted in order to get an alloy of 44 kg containing copper and Zinc in the ratio 3 : 1?

दो मिश्रधातु A और B में क्रमशः 7 : 2 और 5 : 3 के अनुपात में तांबा और जस्ता है। 3 : 1 के अनुपात में तांबा और जस्ता युक्त 44 किलोग्राम मिश्रधातु प्राप्त करने के लिए A और B की कितनी किलोग्राम मात्रा को पिघलाया जाना चाहिए?

Option “D” is correct.

Let x liters is added from alloy A and y liters is added from alloy B.

Then (7x/9) + (5y/8) / (2x/9) + (3y/8) = 3 / 1

⇒ (7x/9) + (5y/8) = (6x/9) + (9y/8)

⇒ [(7x-6x)/9] = [(9y-5y)/8]

⇒ (x/9) = (4y/8)

⇒ (x/y) = (9/2)

⇒ x : y = 9 : 2

Quantity taken from alloy A = (44/11) × 9

⇒ 4 × 9

⇒ 36 kg

Quantity taken from alloy B = (44/11) × 2

⇒ 4 × 2

⇒ 8 kg

∴ 36 kg added from alloy A and 8 kg added from alloy B

29. In a vessel, a mixture of milk and water is in ratio 8 : 7, while in another vessel mixture of milk and water is in ratio 7 : 9. In what ratio mixture of both the vessels should be mixed together so that in the resultant mixture ratio of water and milk becomes 9 : 8?

एक बर्तन में, दूध और पानी का मिश्रण 8 : 7 के अनुपात में है, जबकि दूसरे बर्तन में दूध और पानी का मिश्रण 7 : 9 के अनुपात में है। दोनों बर्तनों के मिश्रणों को किस अनुपात में एक साथ मिलाया जाना चाहिए जिससे कि परिणामी मिश्रण में पानी और दूध का अनुपात 9 : 8 हो जाए?

Option “A” is correct.

Let x litre of the first mixture and y litre of the second mixture are mixed.

Quantity of milk in x litre of the first mixture = 8x/15

Quantity of milk in y litre of the second mixture = 7y/16

Total quantity of the resultant mixture = (x + y)

Quantity of milk in (x + y) litre of the resultant mixture = 8(x + y)/17

8x/15 + 7y/16 = 8(x + y)/17

⇒ 8x/15 + 7y/16 = 8x/17 + 8y/17

⇒ 8x/15 – 8x/17 = 8y/17 – 7y/16

⇒ (136x – 120x)/15 × 17 = (128y – 119y)/17 × 16

⇒ 16x/15 = 9y/16

⇒ 256x = 135y

⇒ x/y = 135/256

 The required ratio is 135 : 256

30. A pot is filled with 3 parts fruit juice and 5 parts with water. By removing how much the amount of the mixture from it and filling the same amount of juice in it, the ratio of fruit juice and water will be 1: 1?

एक बर्तन का 3 भाग फलों के रस से और 5 भाग पानी से भरा है। उसमें से कितने मिश्रण को निकाल कर उसमें उसी मात्रा में फलों के रस भरे जाने से फलों के रस और पानी का अनुपात 1 : 1 हो जाएगा?

Option “B” is correct.

Let the fruit juice and water be 3x and 5x

And, let y amount of mixture be removed

Quantity of fruit juice removed = (3x/8x) × y = 3y/8

Quantity of water removed = (5x/8x) × y = 5y/8

Now, A/Q

(3x – 3y/8 + y)/(5x – 5y/8) = 1/1

⇒ (3x + 5y/8)/(5x – 5y/8) = 1/1

⇒ (3x + 5y/8) = (5x – 5y/8)

⇒ 5y/4 = 2x

⇒ y = 8x/5

The part of mixture removing = (8x/5)/8x = 1/5 part

∴ The amount of mixture which is removing is 1/5 parts.

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