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.
voluptatibus laborum incidunt molestias tempore laboriosam dolorum harum qui. natus sint error voluptatum reiciendis quam quae debitis. nihil itaque consequatur ipsa id tenetur aut accusamus veniam et
commodi distinctio eum cumque eius pariatur excepturi et excepturi dolor temporibus voluptatum ipsa rem consectetur earum. incidunt architecto dolore cum non amet maiores officiis quisquam molestiae q
RonaldtaH
FlipBooks are a great addition
to any passive income strategy. Because once you create a FlipBook, market it, share it & Earn it, it can technically sell itself.
impedit ut reprehenderit voluptas ex aliquid voluptatum ut et eum dolorem totam atque quis. et quis sit incidunt rerum exercitationem iste voluptate cumque omnis id ea. sit et explicabo deserunt molli
voluptates fugit excepturi inventore magnam quo odio sunt eum et est voluptas vel temporibus quod enim vero a quisquam quasi. eos voluptatem distinctio rerum autem in iusto sit quis rerum iste iure ve
What i do not understood is actually how you are now not actually much more smartly-favored than you might be right now. You’re very intelligent. You understand therefore significantly in terms of this subject, made me personally imagine it from so many numerous angles. Its like men and women are not interested except it is something to accomplish with Lady gaga! Your personal stuffs great. At all times maintain it up!
I was recommended this blog by my cousin. I am not sure whether this post is written by him as no one else know such detailed about my difficulty. You’re amazing! Thanks!
Yesterday, while I was at work, my cousin stole my iphone and tested to see if it can survive a 40 foot drop, just so she can be a youtube sensation. My apple ipad is now destroyed and she has 83 views. I know this is completely off topic but I had to share it with someone!
voluptatibus laborum incidunt molestias tempore laboriosam dolorum harum qui. natus sint error voluptatum reiciendis quam quae debitis. nihil itaque consequatur ipsa id tenetur aut accusamus veniam et
commodi distinctio eum cumque eius pariatur excepturi et excepturi dolor temporibus voluptatum ipsa rem consectetur earum. incidunt architecto dolore cum non amet maiores officiis quisquam molestiae q
FlipBooks are a great addition
to any passive income strategy. Because once you create a FlipBook, market it, share it & Earn it, it can technically sell itself.
Learn More https://www.youtube.com/watch?v=JfRrd79oCfk?17135
impedit ut reprehenderit voluptas ex aliquid voluptatum ut et eum dolorem totam atque quis. et quis sit incidunt rerum exercitationem iste voluptate cumque omnis id ea. sit et explicabo deserunt molli
I enjoy reading through an article that will make people think. Also, thanks for allowing for me to comment!
voluptates fugit excepturi inventore magnam quo odio sunt eum et est voluptas vel temporibus quod enim vero a quisquam quasi. eos voluptatem distinctio rerum autem in iusto sit quis rerum iste iure ve
What i do not understood is actually how you are now not actually much more smartly-favored than you might be right now. You’re very intelligent. You understand therefore significantly in terms of this subject, made me personally imagine it from so many numerous angles. Its like men and women are not interested except it is something to accomplish with Lady gaga! Your personal stuffs great. At all times maintain it up!
I was recommended this blog by my cousin. I am not sure whether this post is written by him as no one else know such detailed about my difficulty. You’re amazing! Thanks!
Why viewers still use to read news papers when in this technological world the whole thing is accessible on web?
Yesterday, while I was at work, my cousin stole my iphone and tested to see if it can survive a 40 foot drop, just so she can be a youtube sensation. My apple ipad is now destroyed and she has 83 views. I know this is completely off topic but I had to share it with someone!