141. A beaker contains 80 liters of pure milk. 16 liters of milk is replaced by water and this process repeated further two times. Find the quantity of milk in the final mixture?

एक बर्तन में 80 लीटर शुद्ध दूध है। 16 लीटर दूध को पानी से बदल दिया जाता है और इस प्रक्रिया को दो बार और दोहराया जाता है। अंतिम घोल में दूध की मात्रा ज्ञात कीजिए?

A. 40.96 liters
B. 45.84 liters
C. 48.24 liters
D. 51.72 liters
E. 53.59 liters

Option “A” is correct.

Final quantity of milk = 80 * (1 – 16/80)3

= 40.96 liters

142. A Jar contains 40 liters of apple juice and is replaced 10 liters with water. If the process repeated for one more time from the mixture, then the quantity of apple juice in the final mixture is what percent more than the quantity of water in the final mixture?

एक जार में 40 लीटर सेब का रस होता है और इसे 10 लीटर पानी के साथ प्रतिस्थापित दिया जाता है। यदि यह प्रक्रिया एक और बार दोहराई जाती है, तो अंतिम मिश्रण में सेब के रस की मात्रा, अंतिम मिश्रण में पानी की मात्रा से कितने प्रतिशत अधिक है?

A. 28.57%
B. 42.85%
C. 22.8%
D. 19.87%
E. 23.91%

Option “A” is correct.

First replacement quantity of apple juice = 40 – 10 = 30 liters

Water = 10 liters

Quantity of milk = 40 * (1 – 10/40)2  

= 22.5 liters

 Quantity of water = 40 – 22.5 = 17.5 liters

Required percentage = (22.5 – 17.5)/17.5 * 100 = 28.57%

143. A vessel contains 120 litres of pure wine. x litres of wine is taken out and replaced with same amount of water and the process is repeated one more time and the amount of wine left in the vessel is 67.5 litres. Find the value of ‘x’.

एक बर्तन में 120 लीटर शुद्ध वाइन है। x लीटर वाइन निकाल ली जाती है और उसके स्थान पर उतनी ही मात्रा में पानी डाला जाता है और प्रक्रिया को एक बार और दोहराया जाता है और बर्तन में बची हुई वाइन की मात्रा 67.5 लीटर होती है। ‘x’ का मान ज्ञात करें।

A. 50
B. 20
C. 45
D. 30
E. None of these

Option “D” is correct.

67.5 = 120 (1 – x/120)2

675/1200 = ((120 – x)/120)2

9/16 = ((120 – x)/120)2

(3/4)2 = ((120 – x)/120)2

3/4 = (120 – x)/120

360 = 480 – 4x

x = 30 litres

144. A milkman has 90 litres of milk. 9 litres of milk sold by him and he added same amount of water to the milk. This process is repeated 2 more times. Find the water in the final mixture.

एक दूधवाले के पास 90 लीटर दूध है। 9 लीटर दूध उसके द्वारा बेचा गया और उसने दूध में उतना ही पानी मिलाया। इस प्रक्रिया को 2 बार दोहराया जाता है। अंतिम मिश्रण में पानी की मात्रा ज्ञात करें।

A. 65.61 litres
B. 64.59 litres
C. 16.69 litres
D. 24.39 litres
E. 58.24 litres

Option “D” is correct.

The amount of milk replaced is 10% of total mixture.

The milk in the final mixture = 90 * 90/100 * 90/100 * 90/100 = 65.61

The water in final mixture = 90 – 65.61 = 24.39litres

145. A container contains milk of 80 litres. 12 litres of mixture is taken out and replaced with water. This process was repeated two more times. Find the amount of milk in the final mixture.

एक कंटेनर में 80 लीटर दूध है। मिश्रण का 12 लीटर बाहर निकाला गया है और उसे पानी से प्रतिस्थापित किया गया है। यह प्रक्रिया दो बार दोहरायी गयी थी। अंतिम मिश्रण में दूध की मात्रा को ज्ञात कीजिए।

A. 49.13 litres
B. 43.91 litres
C. 49.31 litres
D. 48.13 litres
E. None of these

Option “A” is correct.

Remaining milk = total milk (1 + (replaced milk/total milk))n

Remaining milk = 80 * (1 – (12/80))3

= 80 * (68/80)3 = 49.13 litres

146.  A milkman has 60 litres mixture of milk and water in the ratio of 7: 5. 24 litres of the mixture is replaced by same quantity of the water and repeated one more time. Find the quantity of the milk in the resultant solution?

एक दूधवाले के पास मिश्रण के 60 लीटर में दूध और पानी 7: 5 के अनुपात में है। मिश्रण के 24 लीटर को पानी की समान मात्रा से प्रतिस्थापित किया गया है और एक अधिक बार फिर दोहराया गया है। परिणामी मिश्रण में दूध की मात्रा को ज्ञात कीजिये?

A. 11.8 litres
B. 12.6 litres
C. 10.2 litres
D. 9.6 litres
E. None of these

Option “B” is correct.

Milk in 60 liters = 7/12 * 60 = 35 litres

Water in 60 liters = 5/12 * 60 = 25 litres

Milk in final solution = 35 * (1 – 24/60)2

= 35 * (36/60)2

= 35 * 3/5 * 3/5

= 12.6 litres

147. A container contains 320 liters acid. 80 liters of acid is taken from the container and replaced with the same quantity of water. This process is repeated 2 more times, find the quantity of acid left in the container?

एक कंटेनर में 320 लीटर एसिड होता है। कंटेनर से 80 लीटर एसिड निकाल लिया जाता है और पानी की समान मात्रा के साथ प्रतिस्थापित किया जाता है। इस प्रक्रिया को 2 बार दोहराया जाता है, कंटेनर में शेष एसिड की मात्रा ज्ञात करें?

A. 135 liters
B. 143 liters
C. 128 liters
D. 148 liters
E. 130 liters

Option “A” is correct.

Required quantity of acid = 320 * (1 – 80/320)3

= 135 liters

148. A vessel contains 120 litres of wine. 30 litres of the wine was taken out of the vessel and replaced by water. Then, 30 litres of mixture was withdrawn and again replaced by water, the operation was repeated for the third time. Find the quantity of wine in the final mixture.

एक बर्तन में 120 लीटर शराब है। बर्तन से 30 लीटर शराब निकाली गई और उसे पानी से बदल दिया गया। फिर, 30 लीटर मिश्रण को निकाला गया और फिर से पानी से बदल दिया गया, यह कार्य को तीसरी बार दोहराया गया। अंतिम मिश्रण में शराब की मात्रा ज्ञात कीजिये।

A. 50.625 liters
B. 50.125 litres
C. 51.625 litres
D. 51.125 litres
E. None of these

Option “A” is correct.

When 30 litres of wine were taken out = 120 – 30 = 90 litres

30 litres of water are added to the mixture.

Ratio of wine to water = 90 : 30 = 3 : 1

30 litres of the mixture is removed.

Remaining mixture = 90 litres

Quantity of wine and water = 67.5 : 22.5

30 litres of water are added.

Quantity of wine and water = 67.5 : 22.5 + 30

= 67.5 : 52.5

The new ratio obtained = 9 : 7

30 litres of the mixture are removed.

Remaining mixture = 90 litres

Quantity of wine and water = 50.625 : 39.375

Wine left in the remaining mixture = 50.625 litres.

149. A jar contains 64 liters of pure milk. One-fourth of the milk is replaced by water. Again the operation is performed. Find the final ratio of milk to water in the jar.

एक जार में 64 लीटर शुद्ध दूध है। एक चौथाई दूध को पानी से बदल दिया जाता है। फिर से यह कार्य किया जाता है। जार में दूध से पानी का अंतिम अनुपात ज्ञात कीजिए।

A. 9:7
B. 1:2
C. 1:9
D. 1:7
E. None of these

Option “A” is correct.

After 2 operations, final quantity of milk = 64 (1 – 1/4)2

= 64 * ¾*3/4

= 36 liters

So quantity of water is 64 – 36 = 28L

So the ratio is 36: 28 = 9: 7

150. A jar has 25 liters of milk. After selling 5 liters of milk, the milkman adds 5 liters of water to the jar. He repeats the process again. What is the percentage of milk contained in the jar now?

एक जार में 25 लीटर दूध होता है। 5 लीटर दूध बेचने के बाद, दूधवाला जार में 5 लीटर पानी मिलाता है। वह फिर से प्रक्रिया को दोहराता है। अब जार में दूध का प्रतिशत कितना है?

A. 16%
B. 64%
C. 32%
D. 14%
E. None of these

Option “B” is correct.

x = Quantity of milk, y = replaced quantity

Amount of milk in the container after n operations = x(1 – y/x)n

= 25(1 – 5/25)2 = 16 liters

Required percentage = 16/25 * 100 = 64%

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