161. A vessel contains 5x liters of pure wine and x liters of pure wine is removed and replaced with water and the process is repeated 2 more times and the quantity of wine left in the vessel is 128 liters. Find the quantity of pure wine.

एक बर्तन में 5x लीटर शुद्ध शराब है और x लीटर शुद्ध शराब को निकाल दिया जाता है और पानी से प्रतिस्थापित किया जाता है और प्रक्रिया को 2 बार और दोहराया जाता है और बर्तन में बची शराब की मात्रा 128 लीटर होती है। शुद्ध शराब की मात्रा ज्ञात कीजिए।

A. 150 liters
B. 200 liters
C. 250 liters
D. 240 liters
E. None of these

Option “C” is correct.

128 = 5x * (1 – x/5x)3

128 = 5x * (4/5)3

128 = 5x * 64/125

x = 50 liters

Quantity of pure wine = 50 * 5 = 250 liters

162. A Jar contains a mixture of beer and water in the ratio of 5:3. If 40 liters of mixture is taken out and 19 liters of water is added to the mixture, then the ratio of beer to water becomes 5:4, then find the quantity of mixture in the Jar initially?

एक जार में बियर और पानी का मिश्रण 5:3 के अनुपात में है। यदि मिश्रण में से 40 लीटर निकाल लिया जाता है और मिश्रण में 19 लीटर पानी मिला दिया जाता है, तो बियर से पानी का अनुपात 5:4 हो जाता है, तो शुरू में जार में मिश्रण की मात्रा ज्ञात कीजिये?

A. 192 liters
B. 160 liters
C. 144 liters
D. 120 liters
E. None of these

Option “A” is correct.

Let the quantity of beer in the Jar initially = 5x

And the quantity of water in the Jar initially = 3x

[5x – 40 * 5/(5 + 3)]/[3x – 40 * 3/(5 + 3) + 19] = 5/4

(5x – 40 * 5/8)/(3x – 40 * 3/8 + 19) = 5/4

(5x – 25) * 4 = (3x – 15 + 19) * 5

20x – 15x = 100 – 75 + 95

5x = 120

x = 24

The quantity of mixture in the Jar initially = (5 + 3) * 24 = 192 liters

163. Vessel A contains milk and water in the ratio of 5:4 and vessel B contains 120 liters of mixture of milk and water in the ratio of 7:5 and x liters mixture of vessel A is added to vessel B, then ratio of milk to water in vessel B becomes 15:11. Find the total quantity of mixture in vessel A, if x liters is 40% of the quantity of mixture in vessel A.

बर्तन A में दूध और पानी का अनुपात 5:4 है और बर्तन B में 120 लीटर दूध और पानी का मिश्रण 7:5 के अनुपात में है और बर्तन A का x लीटर मिश्रण बर्तन B में मिलाया जाता है, तो बर्तन B में दूध से पानी का अनुपात 15:11 हो जाता है। बर्तन A में मिश्रण की कुल मात्रा ज्ञात कीजिए, यदि x लीटर, बर्तन A में मिश्रण की मात्रा का 40% है।

A. 162 liters
B. 90 liters
C. 135 liters
D. 108 liters
E. None of these

Option “B” is correct.

Quantity of milk in vessel B = 120 * 7/12 = 70 liters

Quantity of water in vessel B = 120 – 70 = 50 liters

Quantity of milk added from vessel A = 5x/9

Quantity of water added from vessel A = 4x/9

(70 + 5x/9)/(50 + 4x/9) = 15/11

(630 + 5x)/(450 + 4x) = 15/11

6930 + 55x = 6750 + 60x

5x = 180

x = 36 liters

Total quantity of mixture in vessel A = 36 * 100/40 = 90 liters

164. A vessel contains 200 liters of a mixture of milk and water in the ratio of 3:2. If 25% of the mixture is taken out and y liters of water is added to the mixture, then the quantity of milk and water in the resultant mixture is equal. Find the value of y?

एक बर्तन में 200 लीटर दूध और पानी का मिश्रण 3:2 के अनुपात में है। यदि मिश्रण का 25% निकाल लिया जाता है और मिश्रण में y लीटर पानी मिला दिया जाता है, तो परिणामी मिश्रण में दूध और पानी की मात्रा बराबर है। y का मान ज्ञात कीजिये?

A. 40
B. 10
C. 20
D. 30
E. None of these

Option “D” is correct.

The ratio of the quantity of milk to water in the final mixture = 1:1

The quantity of milk in 200 liters = 200*3/(3+2) = 200*3/5 = 120 liters

The quantity of water in 200 liters = 200 – 120 = 80 liters

25% of the quantity of mixture in 200 liters = 200*25/100 = 50 liters

[120 – 50*3/(3+2)]/[80 – 50*2/(3+2)+y] = 1/1

120 – 50*3/5 = 80 – 50*2/5+y

120-30 = 80 – 20+y

90 = 60+y

y = 30

165. The cost price of variety x wheat is Rs.75 per kg and the cost price of variety y wheat is Rs.82 per kg. If both varieties of wheat are mixed, then the cost price of the mixture is Rs.78 per kg. Find the ratio of the quantity of variety x to variety y wheat.

किस्म x गेहूँ का क्रय मूल्य 75 रुपये प्रति किलो है और किस्म y गेहूं का क्रय मूल्य 82 रुपये प्रति किलो है। यदि दोनों प्रकार के गेहूँ को मिला दिया जाए, तो मिश्रण का क्रय मूल्य 78 रुपये प्रति किग्रा है। किस्म x से किस्म y गेहूं की मात्रा का अनुपात ज्ञात कीजिए।

A. 8:7
B. 7:5
C. 2:1
D. 4:3
E. None of these

Option “D” is correct.

Let the quantity of variety x wheat = a

And the quantity of variety y wheat = b

a * 75 + b * 82 = (a + b) * 78

75a + 82b = 78a + 78b

3a = 4b

a/b = 4/3

166. A vessel contains a mixture of milk and water in which 40% of the mixture is water. If 15 liters of water and 30 liters of milk are added to the mixture, then the quantity of milk becomes 60% more than that of water. Find the initial quantity of the mixture?

एक बर्तन में दूध और पानी का मिश्रण है जिसमें 40% मिश्रण पानी है। यदि मिश्रण में 15 लीटर पानी और 30 लीटर दूध मिला दिया जाए, तो दूध की मात्रा पानी की मात्रा से 60% अधिक हो जाती है। मिश्रण की प्रारंभिक मात्रा ज्ञात कीजिये?

A. 300 liters
B. 100 liters
C. 150 liters
D. 250 liters
E. None of these

Option “C” is correct.

The ratio of the final quantity of milk to water in the mixture = 160:100 = 8:5

The ratio of the initial quantity of milk to water in the mixture = (100 – 40):40 = 60:40 = 3:2

(3x + 30)/(2x + 15) = 8/5

15x + 150 = 16x + 120

x = 30

The initial quantity of mixture = (3 + 2) * 30 = 5 * 30 = 150 liters

167. Jar A, Jar B and Jar C contains the same quantity of mixture of milk and water in the ratio of 3:2, 8:7 and 2:1. If the quantities of all jars are mixed in empty Jar D, the total quantity of milk in Jar D is 270 liters. Find the quantity of water in Jar C?

जार A, जार B और जार C में दूध और पानी के मिश्रण की समान मात्रा 3:2, 8:7 और 2:1 के अनुपात में है। यदि सभी जार की मात्रा को खाली जार D में मिला दिया जाए, तो जार D में दूध की कुल मात्रा 270 लीटर है। जार C में पानी की मात्रा ज्ञात कीजिए?

A. 50 liters
B. 70 liters
C. 60 liters
D. 80 liters
E. None of these

Option “A” is correct.

Quantity of mixture in all jars be x liters.

Quantity of milk in jar D = 3x/5 + 8x/15 + 2x/3 = (9x + 8x + 10x)/15 = 27x/15 = 9x/5

9x/5 = 270

x = 150 liters

Quantity of water in Jar C = 150 * 1/3 = 50 liters

168. A milkman has the mixture of milk and water in the ratio of 5: 3. If he sold 16 liters of the mixture and replaced with same quantity of water, so the ratio becomes 15: 17. What is the initial quantity of the mixture?

एक दूधवाले के पास दूध और पानी का मिश्रण 5:3 के अनुपात में है। यदि वह मिश्रण का 16 लीटर बेच देता है और उसे समान मात्रा में पानी से बदल देता है, तो अनुपात 15:17 हो जाता है। मिश्रण की प्रारंभिक मात्रा क्या है?

A. 48 liters
B. 56 liters
C. 64 liters
D. 80 liters
E. None of these

Option “C” is correct.

Milk in 16 liters = 5/8 * 16 = 10 liters

Water in 16 liters = 3/8 * 16 = 6 liters

(5x – 10)/(3x – 6 + 16) = 15/17

45x + 150 = 85x – 170

40x = 320

x = 8 liters

Total quantity of the mixture = 8 * 8 = 64 liters

169. A vessel contains a mixture of milk and water and the quantity of milk is 80 liters more than that of water. If 80 liters of milk and 40 liters of water is added to the mixture, then the ratio of milk to water becomes 7:4. Find the actual quantity of water in the vessel.

एक बर्तन में दूध और पानी का मिश्रण है और दूध की मात्रा पानी से 80 लीटर अधिक है। यदि मिश्रण में 80 लीटर दूध और 40 लीटर पानी मिला दिया जाए, तो दूध से पानी का अनुपात 7:4 हो जाता है। बर्तन में पानी की वास्तविक मात्रा ज्ञात कीजिए।

A. 120 liters
B. 90 liters
C. 75 liters
D. 100 liters
E. None of these

Option “A” is correct.

Let the actual quantity of water in the vessel = x

And the actual quantity of milk in the vessel = x + 80

(x + 80 + 80)/(x + 40) = 7/4

(x + 160) * 4 = (x + 40) * 7

4x + 640 = 7x + 280

3x = 360

x = 120

Therefore, actual quantity of water in the vessel = 120 liters

170. A Jar contains 150 liters of a mixture of milk and water in the ratio of 3:2. If 50 liters of the mixture is taken out and replaced with the same quantity of milk and 30 liters of water is added to the mixture, then find the ratio of the quantity of milk to water in the resultant mixture?

एक जार में 3:2 के अनुपात में 150 लीटर दूध और पानी का मिश्रण है। यदि 50 लीटर मिश्रण को निकाल कर उतनी ही मात्रा में दूध से बदल दिया जाता है और मिश्रण में 30 लीटर पानी मिला दिया जाता है, तो परिणामी मिश्रण में दूध से पानी की मात्रा का अनुपात ज्ञात कीजिये?

A. 7:5
B. 5:4
C. 9:8
D. 11:7
E. None of these

Option “D” is correct.

The initial quantity of milk in the jar = 150 * 3/(3 + 2) = 150 * 3/5 = 90 liters

The initial quantity of water in the jar = 150 – 90 = 60 liters

The ratio of the quantity of milk to water in the resultant mixture = (90 – 50 * 3/(3 + 2) + 50) : (60 – 50 * 2/(3 + 2) + 30)

= (90 – 50 * 3/5 + 50) : (60 – 50 * 2/5 + 30)

= (90 – 30 + 50) : (60 – 20 + 30)

= 110:70

= 11:7

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