121. The ratio of milk and water in Mixture A is 1:1, if 10 litres of mixture is removed and replaced by milk, the percentage of water in the mixture becomes 45%. Find the amount of milk in mixture A initially?

मिश्रण A में दूध और पानी का अनुपात 1:1 है, यदि 10 लीटर मिश्रण को हटाकर दूध से बदल दिया जाता है, तो मिश्रण में पानी का प्रतिशत 45% हो जाता है। प्रारंभ में मिश्रण A में दूध की मात्रा ज्ञात कीजिए?

A. 50 litres
B. 25 litres
C. 60 litres
D. 90 litres
E. None of these

Option “A” is correct.

Ratio will be 1:1 after removal of 10 litres of mixture.

Let the quantity of milk and water be a litres each after removal

According to question,

(a + 10)/ a = 11/9

9a + 90 = 11a

2a = 90

a = 45

Total mixture after removal = (a + a) = 2 x 45 = 90 litres

Initial mixture = 90 + 10 = 100

Amount of milk in mixture A initially = 1/2 x 100 = 50 litres

122. A milkman has 60 litres of pure milk and then he added 20 litres of the water. If he sold 24 litres of the mixture and then he replaced with water, then what is the ratio of the milk to water in the final mixture?

एक दूधवाले के पास 60 लीटर शुद्ध दूध है और फिर उसने उसमें 20 लीटर पानी मिलाया। यदि उसने मिश्रण का 24 लीटर बेचा और फिर उसे पानी से प्रतिस्थापित कर दिया, तो अंतिम मिश्रण में दूध से पानी का अनुपात क्या है?

A. 18: 17
B. 21: 19
C. 23: 21
D. 24: 23
E. None of these

Option “B” is correct.

Milk = 60 litres

Water = 20 litres

Milk and Water = 60:20 = 3:1

Milk in 24 liters = 3/4* 24 = 18 litres

Water in 24 liters = 1/4 * 24 = 6 litres

Required ratio = (60 – 18)/(20 – 6 + 24)

= 42/38

= 21/19

123. A mixture contains 15 liters of milk and 10 liters of water. What quantity of milk is replaced by water to reverse the ratio of water to milk respectively?

एक मिश्रण में 15 लीटर दूध और 10 लीटर पानी है। पानी से दूध के अनुपात को क्रमशः उलटने के लिए दूध की कितनी मात्रा को पानी से बदल दिया जाता है?

A. 2 liters
B. 5 liters
C. 8 liters
D. 4 liters
E. None of the above

Option “B” is correct.

Quantity of milk = 15 liters

Quantity of water = 10 liters

Let ‘a’ liter milk is replaced by water. Then,

(15-a)/(10+a) = 2/3

45-3a =20+2a

a =5

124. Vessel A contains 60 liters mixture of milk and water in the ratio of 3:2. If 20 liters of mixture is taken out, then find the ratio of the milk and water in the final solution?

बर्तन A में 60 लीटर दूध और पानी का मिश्रण 3:2 के अनुपात में है। यदि 20 लीटर मिश्रण निकाल लिया जाता है, तो अंतिम मिश्रण में दूध और पानी का अनुपात ज्ञात कीजिये?

A. 3:2
B. 2:1
C. 4:3
D. 5:4
E. 1:1

Option “A” is correct.

Milk in 60 liters = 3/5 * 60 = 36 liters

Water in 60 liters = 2/5 * 60 = 24 liters

Milk in 20 liters = 3/5 * 20 = 12 liters

Water in 20 liters = 2/5 * 20 = 8 liters

Required ratio = (36 – 12):(24 – 8)

= 24:16

= 3:2

125. A Jar contains 60 liters of mixture of milk and water. If 60% of the milk is taken out, the quantity of the Jar will be half, what is the initial quantity of the water in the mixture?

एक जार में 60 लीटर दूध और पानी का मिश्रण है। यदि दूध का 60% निकाल लिया जाए, तो जार की मात्रा आधी हो जाएगी, मिश्रण में पानी की प्रारंभिक मात्रा कितनी है?

A. 10 liters
B. 15 liters
C. 20 liters
D. 30 liters
E. None of these

Option “A” is correct.

Milk and Water = 60

Milk * 40/100 + Water =60 * ½ = 30

40Milk + 100water = 3000———(1)

Initially,

Milk + water =60——-(2)

(1)-(2) * 40

60water = 600

Water = 10 liters

126. A vessel contains 60 liters of the mixture of milk and water in the ratio of 2: 1. If 24 liters of the mixture is taken out and replaced by water, then the quantity of the milk in the final mixture is approximately what percent of the quantity of the water in the final mixture?

एक बर्तन में दूध और पानी का 60 लीटर मिश्रण 2:1 के अनुपात में है। यदि मिश्रण में से 24 लीटर निकाल कर उसे पानी से प्रतिस्थापित किया जाता है, तो अंतिम मिश्रण में दूध की मात्रा, अंतिम मिश्रण में पानी की मात्रा का लगभग कितने प्रतिशत होती है?

A. 33.33%
B. 44.44%
C. 66.66%
D. 77.77%
E. 22.22%

Option “C” is correct.

Milk = 2/3 * 60 = 40

Water = 1/3 * 60 = 20

Milk in 24 liters = 2/3 * 24 = 16

Water in 24 liters = 1/3 * 24 = 8 liters

Final quantity of the milk = 40 – 16 = 24

Final quantity of the water = 20 – 8 + 24 = 36

Required percentage = 24/36 * 100 = 66.67%

127. A container contains milk and water, which is in the ratio of 3: 1. If 12 litres of mixture is removed and 8 litres of water is added, then the ratio becomes 1: 3. Find the quantity of milk does the container have initially?

एक कंटेनर में दूध और पानी है, जोकि 3: 1 के अनुपात में है। यदि 12 लीटर मिश्रण को निकाल दिया गया है और 8 लीटर पानी को मिलाया गया है, तो अनुपात 1: 3 हो जाता है। प्रारंभ में कंटेनर में दूध की मात्रा को ज्ञात कीजिये?

A. 12 litres
B. 16 litres
C. 14 litres
D. 10 litres
E. None of these

Option “A” is correct.

The ratio of milk and water in the mixture = 3: 1 (3x, x)

The quantity of milk removed = 12 * (3/4) = 9 litres

The quantity of water removed = 12 – 9 = 3 litres

Given,

(3x – 9) / (x – 3 + 8) = (1/3)

(3x – 9) / (x + 5) = (1/3)

9x – 27 = x + 5

8x = 32

x = 4

Initial quantity of milk = 3x = 12 litres

128. In 90 liters of the mixture of milk and water in the ratio of 7: 3. 20 liters of mixture is taken out and replaced with water. What is the ratio of the milk to water in the final mixture?

90 लीटर मिश्रण में दूध और पानी का अनुपात 7:3 है। इससे 20 लीटर मिश्रण निकाला जाता है और उसे पानी से प्रतिस्थापित किया जाता है, तो अंतिम मिश्रण में दूध से पानी का अनुपात क्या है?

A. 35:31
B. 28:21
C. 49:41
D. 77:71
E. None of these

Option “C” is correct.

Milk = 7/10 * 90 = 63

Water = 3/10 * 90 = 27

Milk in 20 liters of the mixture = 20 * 7/10 = 14

Water in 20 liters of the mixture = 20 * 3/10 = 6

Required ratio = (63 – 14)/(27 – 6 + 20)

= 49/41

129. A milkman has 40 liters of pure milk and then he added 20 liters of the water in that pure milk. If he sold 18 liters of the mixture and then he replaced with water, then what is the ratio of the milk to water in the final mixture?

एक दूधवाले के पास 40 लीटर शुद्ध दूध होता है और फिर उसने उस शुद्ध दूध में 20 लीटर पानी मिलाया। यदि उसने 18 लीटर मिश्रण बेचा और फिर उसे पानी से बदल दिया, तो अंतिम मिश्रण में दूध से पानी का अनुपात क्या है?

A. 1:2
B. 3:4
C. 5:6
D. 7:8
E. None of these

Option “D” is correct.

Milk=40 liters

Water=20 liters

Milk and water=40:20=2:1

Milk in 18 liters of mixture=2/3 * 18=12 liters

Water in the 18 liter mixture=1/3 * 18=6 liters

Milk in the final mixture=40 – 12=28

Water in the final mixture=20 – 6 + 18=32

Required ratio=28:32

=7:8

130. A milkman has 60 liters of the mixture of milk and water in the ratio of x:y and 60% of the milk is taken out from the mixture and 4 liters of the water taken out from the mixture. The final ratio of the milk and water in the mixture is 2:3. Find the ratio of x to y?

एक दूधवाले के पास x:y के अनुपात में दूध और पानी के मिश्रण का 60 लीटर है और मिश्रण से 60% दूध निकाला जाता है और मिश्रण से 4 लीटर पानी निकाला जाता है। मिश्रण में दूध और पानी का अंतिम अनुपात 2:3 है। x से y का अनुपात ज्ञात कीजिये?

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

Option “B” is correct.

The ratio of the milk and water = x: y

x + y=60 ——(1)

(x –( x * 60/100))/(y – 4)=2/3

(5x-3x)/(5y – 20)=2/3

3x=5y-20

5y – 3x=20 ——-(2)

(1) * 5 – ( 2)

8x=280

x =35

y =60 – 35=25

Required ratio = x:y=35:25=7:5

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