41. Two Jars A and B which contains mixture of Milk and Water in the ratio of 4:3 and 1:2 respectively. The Mixture of both Jars is mixed to obtain a mixture of 200 litres, in which quantity of water is 120 litres. Find the ratio of the quantity of mixture in Jar A to quantity of mixture in Jar B?

दो जार A और B जिसमें दूध और पानी का मिश्रण क्रमशः 4:3 और 1:2 के अनुपात में है। दोनों जार के मिश्रण को 200 लीटर का मिश्रण प्राप्त करने के लिए मिलाया जाता है, जिसमें पानी की मात्रा 120 लीटर है। जार A में मिश्रण की मात्रा से जार B में मिश्रण की मात्रा का अनुपात ज्ञात कीजिए?

A. 7:18
B. 6:19
C. 5:21
D. 9:23
E. None of these

Option “A” is correct.

A+B=200 ————– (1)

3A/7+2B/3=120

9A+14B=2520 ——— (2)

(1)*9-(2)

-5B=-720

B=144

A=200-144=56

Required ratio=56:144=7:18

42. The Jar contains 125 litre of the mixture of wine and beer, the ratio of wine and beer is 4:1. 20% of the mixture is removed and added the b litre of beer, the ratio of the wine and beer becomes 1:4. Then w litre of wine added to the mixture, the ratio of the wine and beer becomes 4:1. What is the difference between b and w?

जार में वाइन और बीयर का 125 लीटर मिश्रण है, वाइन और बीयर का अनुपात 4:1 है। मिश्रण का 20% निकाल दिया जाता है और b लीटर बियर मिला दी जाती है, तो वाइन और बियर का अनुपात 1:4 हो जाता है। फिर मिश्रण में w लीटर वाइन मिला दी जाती है, तो वाइन और बीयर का अनुपात 4:1 हो जाता है। b और w में क्या अंतर है?

A. 900 litres
B. 800 litres
C. 1200 litres
D. 600 litres
E. None of these

Option “A” is correct.

20% of the mixture=125*20/100=25 litres

Remaining =125-25=100 litres

Wine=100*4/5=80 litres

Beer=100*1/5=20 litres

80/(20+b)=1/4

320=20+b

b=300 litres

Now the new mixture wine=80 litre and beer=20+300=320 litres

(80+w)/320=4/1

1280=80+w

W=1200 litres

Difference=1200-300=900 litres

43. A vessel contains 400 lit of mixture A consisting of milk and water. 120 lit of this mixture is taken out and mixed with quantity of another mixture B is equal to 150% of mixture of A present in the vessel initially, containing milk and water in the ratio of 3: 2. The quantity of Milk in the mixture A was 60% of the quantity of water in mixture A. Now, 32 Lit of mixture is drawn from final mixture, what is the quantity of water in this quantity of mixture drawn?

एक बर्तन में 400 लीटर मिश्रण A है जिसमें दूध और पानी है। इस मिश्रण का 120 लीटर निकाल लिया जाता है और दूसरे मिश्रण B की मात्रा के साथ मिलाया जाता है, जो शुरू में बर्तन में मौजूद A के मिश्रण के 150% के बराबर होता है, जिसमें दूध और पानी 3: 2 के अनुपात में होता है। मिश्रण A में दूध की मात्रा, मिश्रण A में पानी की मात्रा का 60% था। अब, अंतिम मिश्रण से 32 लीटर मिश्रण निकाला जाता है, निकाले गए मिश्रण की इस मात्रा में पानी की मात्रा कितनी है?

A. 22
B. 24
C. 20
D. 14
E. 16

Option “D” is correct.

Mixture A = 400 lit

The quantity of Milk in the mixture A was 60% of the quantity of water in mixture A

Hence ratio of Milk and water in the mixture A is ‘

60: 100 = 3: 5

Milk = 3/8 * 400 =150

Water = 400 – 150 = 250

Mixture B contains Milk and water in the ratio = 3: 2

Mixture B of quantity equal to 150% of mixture of A present in the vessel initially

Mixture B = 600 Lit

Milk in B = 360 and Water in B = 240

In 120 lit of Mixture A, Milk = 3/8 * 120 = 45

Water = 75, Mixed is Mixture B.

Now total milk in B = 360 + 45 = 405

Total water in B = 240 + 75 = 315

Ratio of Milk and water = 405: 315

= 9: 7

Quantity of water in 32 Lit of mixture drawn = 7/16 * 32

=14 Lit

44. A container contains ______________ litres mixture which contains milk and water in the ratio 6:5. The milkman sold 33 litres of the mixture and added 5 litres of milk to the remaining mixture. Quantity of milk in the final mixture is _____________.

एक कंटेनर में __________ लीटर मिश्रण होता है जिसमें दूध और पानी का अनुपात 6:5 है। दूधवाले ने मिश्रण का 33 लीटर बेचा और शेष मिश्रण में 5 लीटर दूध मिला दिया। अंतिम मिश्रण में दूध की मात्रा _________ है।

A. 55, 15
B. 88, 35
C. 77, 40
D. 66, 25
E. None of these

Option “B” is correct.

Option (A)

Total quantity of mixture = 55 litres

Quantity of milk in the initial mixture = 6/11 x 55 = 30 litres

Quantity of milk in the final mixture = 30 – 6/11 x 33 + 5

= 30 – 18 + 5

= 17 litres

This does not satisfy the given condition.

Option (B)

Total quantity of mixture = 88 litres

Quantity of milk in the initial mixture = 6/11 x 88 = 48 litres

Quantity of milk in the final mixture = 48 – 6/11 x 33 + 5

= 48 – 18 + 5

= 35 litres

This satisfies the given condition.

Option (C)

Total quantity of mixture = 77 litres

Quantity of milk in the initial mixture = 6/11 x 77 = 42 litres

Quantity of milk in the final mixture = 42 – 6/11 x 33 + 5

= 42 – 18 + 5

= 29 litres

This does not satisfy the given condition.

Option (D)

Total quantity of mixture = 66 litres

Quantity of milk in the initial mixture = 6/11 x 66 = 36 litres

Quantity of milk in the final mixture = 36 – 6/11 x 33 + 5

= 36 – 18 + 5

= 23 litres

This does not satisfy the given condition.

45. A shopkeeper mixes two types of Rice costing Rs.50/kg and Rs.75/Kg in the ratio of 3: 5 in container A. He mixes two types of wheat costing Rs.60/Kg and Rs.80/Kg in the ratio of 1: 3 in container B. Average cost of rice in container A is what percentage of the average cost of wheat in container B?

एक दुकानदार कंटेनर A में 3:5 के अनुपात में 50 रुपये/किलोग्राम और 75 रुपये/किलोग्राम के दो प्रकार के चावल मिलाता है। वह कंटेनर B में 1:3 के अनुपात में 60 रुपये/किलोग्राम और 80 रुपये/किलोग्राम के दो प्रकार के गेहूं मिलाता है। कंटेनर A में चावल की औसत लागत कंटेनर B में गेहूं की औसत लागत का कितना प्रतिशत है?

A. 86.2%
B. 87.5%
C. 85.4%
D. 82.5%
E. None of these

Option “B” is correct.

Let, average cost of rice in container A = Rs. k

And average cost of wheat in container B = Rs. n

(75 – k)/(k – 50) = 3/5

=> 375 – 5k = 3k – 150

=> 5k + 3k = 375 + 150

=> 8k = 525

=> k = 525/8

=> k = Rs.65.625

(80 – n)/(n – 60) = 1/3

=> 240 – 3n = n – 60

=> 3n + n = 240 + 60

=> 4n = 300

=> n = 300/4

=> n = Rs.75

Required percentage = 65.625/75 x 100 = 87.5%

46. Vessel A contains 98 litres mixture which contains milk and water in the ratio 4:3 respectively. Vessel B contains 85 litres mixture which contains milk and water in the ratio 3:2 respectively. Contents of vessel A and vessel B are emptied and filled into vessel C and seven litres more milk and four litres more water are added to it. Find the final ratio of milk and water in container C.

बर्तन A में 98 लीटर मिश्रण है जिसमें दूध और पानी का अनुपात क्रमशः 4:3 है। बर्तन B में 85 लीटर मिश्रण है जिसमें दूध और पानी का अनुपात क्रमश: 3:2 है। बर्तन A और बर्तन B की सामग्री को खाली कर दिया जाता है और बर्तन C में भर दिया जाता है और इसमें सात लीटर दूध और चार लीटर अधिक पानी मिला दिया जाता है। कंटेनर C में दूध और पानी का अंतिम अनुपात ज्ञात कीजिए।

A. 77:50
B. 67:30
C. 57:40
D. 37:20
E. None of these

Option “C” is correct.

Quantity of milk in container A = 4/7 x 98 = 56 litres

Quantity of water in container A = 3/7 x 98 = 42 litres

Quantity of milk in container B = 3/5 x 85 = 51 litres

Quantity of water in container B = 2/5 x 85 = 34 litres

Final quantity of milk in container C = 56 + 51 + 7 = 114 litres

Final quantity of water in container C = 42 + 34 + 4 = 80 litres

Required ratio = 114 : 80 = 57:40

47. A container contains 133 litres mixture which contains wine and water in the ratio 11:8 respectively. 76 litres of the mixture used in a reception party and 7 litres pure wine and 6 litres water added to the container. Find the difference between the quantity of wine and quantity of water in the final mixture.

एक कंटेनर में 133 लीटर का मिश्रण है जिसमें क्रमशः 11:8 के अनुपात में वाइन और पानी है। रिसेप्शन पार्टी में मिश्रण का 76 लीटर उपयोग किया गया और कंटेनर में 7 लीटर शुद्ध वाइन और 6 लीटर पानी मिलाया जाता है। अंतिम मिश्रण में वाइन की मात्रा और पानी की मात्रा के बीच का अंतर ज्ञात कीजिए।

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

Option “B” is correct.

Quantity of wine in the initial mixture = 11/19 x 133 = 77 litres

Quantity of water in the initial mixture = 8/19 x 133 = 56 litres

Quantity of wine in the final mixture = 77 – 11/19 x 76 + 7

= 77 – 44 + 7

= 40 litres

Quantity of water in the final mixture = 56 – 8/19 x 76 + 6

= 56 – 32 + 6

= 30 litres

Required difference = 40 – 30 = 10 litres

48. A 132 litres mixture contains milk and water in the ratio 6:5 respectively. The milk man sold 44 litres of mixture and added ___________ litres pure milk and __________ litres water to the remaining mixture. The ratio of milk and water in the final mixtures becomes 6:5.

132 लीटर के मिश्रण में दूध और पानी का अनुपात क्रमशः 6:5 है। दूधवाले ने 44 लीटर मिश्रण बेचा और शेष मिश्रण में __________ लीटर शुद्ध दूध और __________ लीटर पानी मिला दिया। अंतिम मिश्रण में दूध और पानी का अनुपात 6:5 हो जाता है।

Which of the following options satisfy the given condition?
निम्नलिखित में से कौन सा विकल्प दी गई शर्त को पूरा करता है?

I. 12, 10

II. 6, 5

III. 6, 4

A. Only I
B. Only II
C. Only III
D. Both I and II
E. Both II and III

Option “D” is correct.

Quantity of milk in the initial mixture = 6/11 x 132 = 72 litres

Quantity of water in the initial mixture = 5/11 x 132 = 60 litres

Quantity of milk in the remaining mixture = 72 – 6/11 x 44 = 72 – 24 = 48 litres

Quantity of water in the remaining mixture = 60 – 5/11 x 44 = 60 – 20 = 40 litres

I.

(48 + 12)/(40 + 10) = 60/50 = 6/5

This satisfies the given condition.

II.

(48 + 6)/(40 + 5) = 54/45 = 6/5

This satisfies the given condition.

III.

(48 + 6)/(40 + 4) = 54/44 = 27/22 ≠ 6/5

This does not satisfy the given condition.

49. A can contains a mixture of two liquids A and B in the ratio 5: 3. When 4 liters of mixture are drawn off and replaced with liquid B, the ratio of A and B becomes 5: 7. How many liters of liquid A was contained by the can initially?

A में दो तरल A और B का मिश्रण 5:3 के अनुपात में है। जब 4 लीटर मिश्रण निकाला जाता है और तरल B से प्रतिस्थापित किया जाता है, तो A और B का अनुपात 5:7 हो जाता है। प्रारंभ में बर्तन में कितने लीटर तरल A था?

A. 6
B. 7.5
C. 8
D. 4.5
E. None of these

Option “B” is correct.

Let the can contains 5x and 3x of mixtures A and B respectively.

Quantity of A in mixture left = 5x – 5 * 4/8 = (5x – 5/2) liters

Quantity of B in mixture left = 3x – 3 * 4/8 = (3x – 3/2) liters

=> (5x – 5/2)/ [(3x – 3/2) + 4] = 5/7

=> (10x – 5)/(6x + 5) = 5/7

=> 70x – 35 = 30x + 25

=> x = 3/2

The can initially has 5x = 5 * 3/2 = 7.5 liters of liquid A

50. Vessel A contains 60 liters mixture of milk and water in the ratio of 1:2. If 24 liters of mixture is taken out from vessel A in the ratio of 3:5 and poured into vessel B, then the final quantity of milk in vessel A is what percent of the final quantity of water in vessel A?

बर्तन A में 1:2 के अनुपात में 60 लीटर दूध और पानी का मिश्रण है। यदि बर्तन A से 3:5 के अनुपात में 24 लीटर मिश्रण निकाला जाता है और बर्तन B में डाला जाता है, तो बर्तन A में दूध की अंतिम मात्रा बर्तन A में पानी की अंतिम मात्रा का कितना प्रतिशत है?

A. 42%
B. 44%
C. 46%
D. 48%
E. 50%

Option “B” is correct.

Initial quantity of milk in vessel A = 60 * 1/3 = 20 liters

Initial quantity of water in vessel A = 60 * 2/3 = 40 liters

Milk in 24 liters = 3/8 * 24 = 9 liters

Water in 24 liters = 5/8 * 24 = 15 liters

Final quantity of milk in vessel A = 20 – 9 = 11 liters

Final quantity of water in vessel A = 40 – 15 = 25 liters

Required percentage = 11/25 * 100 = 44%

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