131. A container contains 156 litres mixture which contains milk and water in the ratio of 7: 6. The milkman sold 52 litres of the mixture and added 64 litres of another mixture of milk and water which contains milk and water in the ratio of 5: 3 into it. Find the difference between amount of milk and amount of water in the final mixture.

एक कंटेनर में दूध और पानी का 156 लीटर मिश्रण है जिसमें दूध और पानी 7: 6 के अनुपात में है। दूधवाले ने 52 लीटर मिश्रण का विक्रय किया और दूध और पानी के दूसरे मिश्रण के 64 लीटर, जिसमें दूध और पानी 5: 3 के अनुपात में है, को मिलाया। अंतिम मिश्रण में दूध की मात्रा और पानी की मात्रा के बीच का अंतर ज्ञात कीजिए।

A. 20 litres
B. 24 litres
C. 30 litres
D. 36 litres
E. None of these

Option “B” is correct.

Quantity of milk in the initial mixture = 7/13 x 156 = 84 litres

Quantity of water in the initial mixture = 6/13 x 156 = 72 litres

Quantity of milk in the final mixture = 84 – 7/13 x 52 + 5/8 x 64 = 96 litres

Quantity of water in the final mixture = 72 – 6/13 x 52 + 3/8 x 64 = 72 litres

Required difference = 96 – 72 = 24 litres

132. A beaker contains a mixture of diesel and petrol in the ratio of 4:5. If 18 liters of mixture is taken out and added 2 liters of diesel, then the ratio of the diesel to petrol becomes 5:6 and again 22 liters of mixture is taken out and added 8 liters of petrol, then find the ratio of the diesel to petrol in the final mixture?

एक बीकर में डीजल और पेट्रोल का मिश्रण 4:5 के अनुपात में है। यदि 18 लीटर मिश्रण को निकाल कर 2 लीटर डीजल से प्रतिस्थापित किया जाता है तो डीजल से पेट्रोल का अनुपात 5:6 हो जाता है और फिर से 22 लीटर मिश्रण निकालकर 8 लीटर पेट्रोल से प्रतिस्थापित किया जाता है, तो अंतिम मिश्रण में डीजल से पेट्रोल का अनुपात ज्ञात कीजिए?

A. 5:7
B. 5:6
C. 5:8
D. 5:9
E. 4:5

Option “A” is correct.

Diesel in 18 liters = 4/9 * 18 = 8 liters

Petrol in 18 liters = 5/9 * 18 = 10 liters

(4x – 8 + 2)/(5x – 10) = 5/6

25x – 50 = 24x – 48 + 12

x = 14

Diesel = 14 * 4 – 8 + 2 = 50

Petrol = 5 * 14 – 10 = 60

Diesel in 22 liters = 5/11 * 22 = 10 liters

Petrol in 22 liters = 6/11 * 22 = 12 liters

Required ratio = 50 – 10:60 – 12 + 8

= 40:56

= 5:7

133. 144 liters mixture contains apple and orange juice in the ratio of 7:5. If 60 liters of mixture is taken out and then (x + 16) liters of apple juice and x liters of orange juice is added in the remaining mixture, now the ratio of the apple to orange juice becomes 8:5, find the value of x?

144 लीटर मिश्रण में सेब और संतरे का रस 7:5 के अनुपात में है। यदि 60 लीटर मिश्रण निकाला जाता है और फिर (x + 16) लीटर सेब का रस और x लीटर संतरे का रस शेष मिश्रण में मिलाया जाता है, तो अब सेब और संतरे के रस का अनुपात 8:5 हो जाता है, x का मान ज्ञात कीजिए?

A. 12
B. 10
C. 15
D. 20
E. 25

Option “C” is correct.

Apple in 144 liters = 7/12 * 144 = 84

Orange in 144 liters = 5/12 * 144 = 60 liters

Apple in 60 liters = 7/12 * 60 = 35

Orange in 60 liters = 5/12 * 60 = 25 liters

(84 – 35 + (x + 16))/(60 – 25 + x) = 8/5

280 + 8x = 245 + 5x + 80

x = 15

134. Kowsick had some quantity of coke. He drunk 15% of coke and replaced with water. He then drunk 20% of mixture and replaced with water. Finally, he drunk 30% of mixture and replaced with water. If he was left with 1904 ml of coke, then initially, how much coke did he have?

कौसिक के पास कुछ मात्रा में कोक था। उसने 15% कोक पिया और उसकी जगह पानी मिलाया। फिर उसने 20% मिश्रण पिया और उसके स्थान पर पानी मिलाया। अंत में, उसने 30% मिश्रण पिया और उसके स्थान पर पानी मिलाया। यदि उसके पास 1904 मिली कोक बचा था, तो शुरू में उसके पास कितना कोक था?

A. 4.2 litres
B. 4 litres
C. 4.5 litres
D. 5.6 litres
E. 4.8 litres

Option “B” is correct.

Let Kowsick had ‘a’ ml coke After the first process, the quantity of coke left = 85% of a

= 0.85a ml

After the 2nd process, the quantity of coke left = 80% of 0.85a = 0.68a

After the third process, the quantity of coke left = 70% of 0.68a = 0.476a = 1904

a = 1904/0.476 = 4000 ml = 4 litres

Short cut:

The initial quantity of coke = 1904 * 100/70 * 100/80 * 100/85 = 4000 ml

= 4 litres

135. A Vessel contains a mixture of milk and water and the amount of milk is 62.5% of the vessel. If 72 liters of mixture is taken out and 15 liters of milk and three liters of water are added to the remaining solution, then the quantity of water becomes half of the milk. Find the initial quantity of the mixture in the vessel?

एक बर्तन में दूध और पानी का मिश्रण है और दूध की मात्रा बर्तन का 62.5% है। यदि 72 लीटर मिश्रण निकाल दिया जाता है और शेष घोल में 15 लीटर दूध और तीन लीटर पानी मिला दिया जाता है, तो पानी की मात्रा दूध की आधी हो जाती है। बर्तन में मिश्रण की प्रारंभिक मात्रा ज्ञात कीजिये?

A. 120
B. 136
C. 144
D. 160
E. None of these

Option “C” is correct.

Initial quantity = 100x

Milk = 62.5/100 * 100x = 62.5x

Water = 100x – 62.5x = 37.5x

Milk in 72 liters = 72 * 62.5x/100x = 45 liters

Water in 72 liters = 72 * 37.5x/100x = 27 liters

(62.5x – 45 + 15)/(37.5x – 27 + 3) = 100/50

75x – 48 = 62.5x – 30

x = 1.44

Quantity of vessel = 100 * 1.44 = 144 liters

136. A vessel contains milk and water, in which 30% is water. 20 litres of mixture was taken out and replaced by water and the ratio becomes 77: 53. Find the initial quantity of milk in the vessel?

एक बर्तन में दूध और पानी है, जिसमें 30% पानी है। 20 लीटर मिश्रण को निकाल कर पानी से बदल दिया गया और अनुपात 77:53 हो जाता है। बर्तन में दूध की प्रारंभिक मात्रा ज्ञात कीजिये?

A. 91 litres
B. 98 litres
C. 84 litres
D. 105 litres
E. None of these

Option “A” is correct.

The ratio of milk and water = 70 : 30 = 7 : 3

The quantity of milk taken out = 20*(7/10) = 14 litres

The quantity of milk taken out = 20*(3/10) = 6 litres

Given,

(7x – 14) / (3x – 6 + 20) = (77/53)

371x – 742 = 231x + 1078

140x = 1820

x = 13

The initial quantity of milk in the vessel = 7x = 91 litres

137. 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.

138. 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.

139. 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

140. 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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