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1) 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 mixture?
A.3:2
B.2:1
C.4:3
D.5:4
E.1:1
2) Vessel A contains the mixture of milk and water in the ratio of 3:2. If 20 liters are taken out and added 4 liters of water, then the ratio of the milk and water becomes 6:5. Find the initial quantity of the mixture?
A.50
B.40
C.80
D.60
E.90
3) A vessel contains 60 liters mixture of milk and water in the ratio of 7:5. If certain quantity of mixture is taken out and filled with 13 liters of water, then the ratio of the water and milk becomes 4:3, then find the quantity of water in the final solution?
A.20 liters
B.24 liters
C.28 liters
D.32 liters
E.None of these
4) A mixture of oil and water contains 40% water. If 6 liters of oil is taken out from the mixture, then the quantity of oil and water becomes same, then find the initial quantity of the mixture?
A.30 liters
B.40 liters
C.45 liters
D.50 liters
E.None of these
5) Vessel A contains 60 liters mixture of milk and water in the ratio of 3:2 and vessel B contains x liters mixture of milk and water in the ratio of 5:4. If vessel A and B are mixed, then the ratio of the milk and water in the resultant mixture is 7:5. Find the value of x?
A.45
B.54
C.36
D.90
E.72
6) A Jar contains a 120 liters mixture of oil and water in the ratio of 3:2. If 25% of the mixture is taken out and replaced with water, then find the ratio of oil and water in the final solution?
A.9:11
B.1:2
C.3:4
D.7:11
E.2:1
7) A vessel contains a mixture of milk and water, containing 45% of water. 120 liters of mixture is taken out from the vessel and filled with 4 liters of water and then the quantity of the milk in the final solution is 10% more than that of water. Find the quantity of water in the final solution?
A.30 liters
B.40 liters
C.50 liters
D.60 liters
E.70 liters
8) Vessel A contains 75 liters mixture of milk and water and the quantity of water is 32% of the total quantity of mixture. Vessel B contains 90 liters mixture of milk and water and the quantity of milk is 175% more that of the water. If vessel A and B mixture are mixed together and then added x liters of water and now the ratio of the milk and water in the final mixture becomes 2:1, find the value of x?
A.12.5
B.10.5
C.13.5
D.14.5
E.16.5
9) A vessel contains 180 liters mixture of milk and water is in the ratio of 2: 1. How much quantity of water should be added, so that the percentage of milk in the vessel becomes 60% of the total mixture?
A.10 liters
B.20 liters
C.15 liters
D.25 liters
E.None of these
10) A mixture contains oil and water in the ratio of 5:3. If 120 liters of mixture is taken out and 25 liters of oil and 5 liters of water is added in the remaining mixture, then the ratio of the oil to water becomes 2:1. Find the initial quantity of mixture?
A.160 liters
B.200 liters
C.240 liters
D.280 liters
E.320 liters
Answers :
1) Answer: A
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
2) Answer: D
Milk in 20 liters = 3/5 * 20 = 12 liters
Water in 20 liters = 2/5 * 20 = 8 liters
(3x – 12)/(2x – 8 + 4) = 6/5
15x – 60 = 12x – 24
x = 12
Quantity of mixture = 12 * 5 = 60 liters
3) Answer: C
Milk in 60 liters = 60 * 7/12 = 35
Water in 60 liters = 60 * 5/12 = 25
(35 – 7x/12)/(25 – 5x/12 + 13) =3/4
114 – 5x/4 = 140 – 7x/3
7x/3 – 5x/4 = 26
x = 24
Final quantity of water = 25 – (5 * 24/12) + 13 = 28 liters
4) Answer: A
Initial quantity of mixture = 100x
Oil = 100x * 60/100 = 60x
Water = 40/100 * 100x = 40x
(60x – 6)/40x = 1/1
60x – 6 = 40x
20x = 6
100x = 6 * 5 = 30
5) Answer: C
Milk vessel A = 60 * 3/5 = 36
Water in vessel A = 60 * 2/5 = 24
(36 + 5x/9)/(24 + 4x/9) = 7/5
168 + 28x/9 = 180 + 25x/9
3x/9 = 12
x = 36
6) Answer: A
Oil = 3/5 * 120 = 72 liters
Water = 2/5 * 120 = 48 liters
25% of mixture = 25/100 * 120 = 30
Oil in 30 liters = 30 * 3/5 = 18
Water in 30 liters = 30 * 2/5 = 12
Required ratio = (72 – 18): (48 – 12 + 30)
= 54:66
= 9:11
7) Answer: B
The initial quantity of milk = 55x
The initial quantity of water = 45x
Milk in 120 liters = 55/100 * 120 = 66 liters
Water in 120 liters = 45/100 * 120 = 54 liters
(55x – 66)/(45x – 54 + 4) = 110/100
495x – 550 = 550x – 660
x = 2
Final quantity of water = 45 * 2 – 50 = 40 liters
8) Answer: B
Milk in Vessel A = 75 * 68/100 = 51
Water in Vessel A = 75 * 32/100 = 24
Ratio of milk and water in B = 275:100 = 11:4
Milk in Vessel B = 90 * 11/15 = 66
Water in Vessel B = 90 * 4/15 = 24
(51 + 66)/(24 + 24 + x) = 2/1
96 + 2x = 117
x = 10.5
9) Answer: B
Milk = 2/3 * 180 = 120Liters
Water = 180 – 120 = 60Liters
120 = (180 + x) * 60%
12000=10800+60x
1200=60x
=> x = 20Liters
10) Answer: C
Initial quantity = 8x
Oil = 5x
Water = 3x
Oil in 120 liters = 120 * 5/8 = 75 liters
Water in 120 liters = 120 * 3/8 = 45 liters
(5x – 75 + 25)/(3x – 45 + 5) = 2/1
6x – 80 = 5x – 50
x = 30
Initial quantity = 8 * 30 = 240 liters
11) Vessel A contains 60 liters mixture of milk and water in the ratio of 3:2 and vessel B contains x liters mixture of milk and water in the ratio 6:5. If vessel A and B’s mixture is mixed, then the ratio of the milk and water in the resultant solution is 15:11, then find the value of x?
A.33
B.44
C.55
D.66
E.None of these
12) The vessel contains 45 liters of milk and water in the ratio of 5:4. If x liters of water is added to the mixture and the ratio of the water and milk ratio becomes 5:4, then find the value of x?
A.12.5
B.13.5
C.11.5
D.10.5
E.None of these
13) A vessel has 30 liters mixture of milk and water in the ratio of 3: 2. If x liters of water and 22 liters of milk added to the mixture, then the ratio of the milk to water becomes 4: 5. Find the value of x?
A.28
B.18
C.36
D.45
E.None of these
14) If vessel A contains the mixture of milk and water in the ratio of 4: 3 and vessel B contains 60 litres of mixture of milk and water in the ratio of 7: 5. If the vessel A and B’s mixture is mixed, then the ratio of the milk to water becomes 11: 8, then find the initial quantity of mixture in vessel A?
A.35 litres
B.28 litres
C.56 litres
D.63 litres
E.None of these
15) How many Kg of sugar costing Rs.36/kg must be mixed with 20 kg of sugar costing Rs.50/kg, so that the shopkeeper obtained a profit of 25% by selling the mixture at Rs.50/kg?
A.40 kg
B.30 kg
C.50 kg
D.60 kg
E.None of these
16) A Jar contains 40 liters mixture of milk and water in the ratio of 3: 2 and x liters of mixture is taken out and 20 liters of water added, then the ratio of the milk and water becomes 3: 7. Find the value of x?
A.10
B.15
C.20
D.25
E.None of these
17) A milkman has 45 liters mixture of milk and water in the ratio of 3: 2. If he sold x liters of mixture and replaced by water, then the ratio of milk and water becomes 1: 2, find the value of x?
A.15 liters
B.10 liters
C.30 liters
D.20 liters
E.None of these
18) Vessel A, B and C contains the mixture of milk and water in the ratio of 3:2, 5:4 and 2:1 respectively. If all the vessel mixtures are mixed, then find the ratio of milk and water in the final mixture?
A.82:53
B.82:55
C.80:53
D.81:53
E.None of these
19) A vessel contains the mixture of milk and water in the ratio of 4: 1. If 25 liters of water is added to the vessel, then the ratio of the milk and water becomes 16: 9, what is the initial quantity of the mixture?
A.50 liters
B.75 liters
C.100 liters
D.150 liters
E.None of these
20) A vessel contains 60 liters milk. If x liters of milk is taken out and replaced by water, this process is repeated two more times and then the quantity of the water in the vessel is 29.28 liters, find the value of x?
A.10
B.12
C.15
D.18
E.20
Answers :
11) Answer: B
Milk in vessel A = 3/5 * 60 = 36 liters
Water in vessel A = 2/5 * 60 = 24 liters
(36 + 6x/11)/(24 + 5x/11) = 15/11
(396 + 6x) * 11 = 15 * (264 + 5x)
396 = 9x
x = 44 liters
12) Answer: E
Milk = 5/9 * 45 = 25 liters
Water = 4/9 * 45 = 20 liters
25/(20 + x) = 4/5
80 + 4x = 25 * 5
4x = 45
x = 11.25 liters
13) Answer: E
Milk = 3/5 * 30 = 18 liters
Water = 2/5 * 30 = 12 liters
(18 + 22)/(12 + x) = 4/5
40/(12 + x) = 4/5
x = 38 liters
14) Answer: A
Milk in vessel B = 7/12 * 60 = 35 liters
Water in vessel B = 5/12 * 60 = 25 liters
Let us take the quantity of mixture in vessel A be x
(4x/7 + 35)/(3x/7 + 25) = 11/8
33x/7 + 275 = 32x/7 + 280
x/7 = 5
x = 35 litres
15) Answer: C
CP of the mixture = 50/125 * 100 = 40
= (50 – 40): (40 – 36) = 10: 4 = 5: 2
5: 2 = x: 20
x = 50 kg
16) Answer: C
Milk in 40 liters = 3/5 * 40 = 24 liters
Water in 40 liters = 2/5 * 40 = 16 liters
(24 – (3x/5))/(16 – (2x/5) + 20) = 3/7
(120 – 3x)/(180 – 2x) = 3/7
540 – 6x = 840 – 21x
15x = 300
x = 20 liters
17) Answer: D
Milk in 45 liters = 3/5 * 45 = 27 liters
Water in 45 liters = 2/5 * 45 = 18 liters
(27 – 3x/5)/(18 – 2x/5 + x) = ½
90 – 2x + 5x = 270 – 6x
9x = 180
x = 20 liters
18) Answer: A
Required ratio = (3/5 + 5/9 + 2/3):(2/5 + 4/9 + 1/3)
= (27 + 25 + 30):(18 + 20 + 15)
= 82:53
19) Answer: C
4x/(x + 25) = 16/9
16x + 25 * 16 = 36x
20x = 400
x = 20
Total quantity = 20 * 5 = 100 liters
20) Answer: B
60 * (1 – (x/60))3 = 60 – 29.28
60 * (1 – (x/60))3 = 30.72
(1 – x/60)3 = 512/1000
1 – x/60 = 8/10
x = 12 liters
21) Ratio of the mixture of milk and water in Jar A is 3:2 and the ratio of the mixture of milk and water in Jar B is 4:3. If both mixtures are mixed in Jar C, then what is the ratio of the milk and water in Jar C?
A.44:29
B.41:27
C.41:29
D.43:29
E.None of these
22) A Jar contains 5x litres of the mixture of milk and water in the ratio of 3: 2 and 20 litres of the mixture is taken out. Then added 24 litres of the water in the remaining mixture, the ratio of the milk and water becomes 1: 2. Find the value of 5x?
A.40
B.50
C.60
D.30
E.None of these
23) Vessel A contains 70 liters mixture of milk and water in the ratio of 4:1 and vessel B contains 90 liters mixture of milk and water in the ratio of 5:4. If both mixtures are mixed, then what is the percentage of the milk in the final mixture?
A.72.67%
B.66.25%
C.59.50%
D.48.72%
E.None of these
24) How many litres of water should be added to 80 litres of mixture containing milk and water in the ratio of 3: 2, such that the resultant mixture has 50 % milk in it?
A.24 litres
B.20 litres
C.28 litres
D.16 litres
E.None of these
25) A milkman has the mixture of milk and water in the ratio of 5:3. If he sold 16 liters of the mixture and added 16 liters of the water to the mixture, so the ratio becomes 15:17. What is the initial quantity of the mixture?
A.48 liters
B.56 liters
C.64 liters
D.80 liters
E.None of these
26) A Vessel contains 60 liters of milk and water in the ratio of 4: 1. If 20 liters of mixture is taken out, then x liters of the milk are added to the remaining mixture, now the ratio of milk to water becomes is 5: 1. Find the value of x?
A.12
B.8
C.6
D.10
E.None of these
27) A milkman has 64 liters mixture of milk and water in the ratio of 5: 3. X liters of mixture taken out and replaced with water, now the resultant ratio of the milk to water is 25: 39. Find the value of x?
A.8
B.16
C.32
D.24
E.None of these
28) How many kg of variety 1 rice costing Rs. 52/kg should mixed with 25 kg of variety 2 rice costing Rs. 58 per kg, so that he makes a profit of 25% on selling the mixture at Rs. 67.5/kg?
A.40 kg
B.60 kg
C.50 kg
D.70 kg
E.None of these
29) A milkman has 80 litres mixture of milk and water in the ratio of 11: 9. If he sold 40 litres of mixture and then he filled with 8 liters of milk and x litres of water, now the ratio of the milk and water is 1: 1. Find the value of x?
A.10 litres
B.12 litres
C.14 litres
D.16 litres
E.None of these
30) A vessel contains the mixture of milk and water in the ratio of 5: 4. If 36 liters of mixture is taken out and then 10 liters of water added to the remaining mixture, now the ratio of the milk and water becomes 5: 6. Find the initial quantity of the mixture?
A.36 liters
B.45 liters
C.63 liters
D.81 liters
E.None of these
Answers :
21) Answer: C
Milk in Jar A = 3/5
Water in Jar A = 2/5
Milk in Jar B = 4/7
Water in Jar B = 3/7
Milk and water in Jar C = (3/5 + 4/7):(2/5 + 3/7)
=(21 + 20):(14 + 15)
= 41:29
22) Answer: B
Milk in 20 litres = 3/5 * 20 = 12 litres
Water in 20 litres = 2/5 * 20 = 8 litres
(3x – 12)/(2x – 8 + 24) = 1/2
2x + 16 = 6x – 24
4x = 40
x = 10 litres
Total mixture = 5 * 10 = 50 litres
23) Answer: B
Milk in vessel A = 70 * 4/5 = 56 liters
Milk in vessel B = 90 * 5/9 = 50 liters
Required percentage = [(56 + 50)/(70 + 90)] *100
= 66.25%
24) Answer: D
Total mixture = 80 litres
The milk and water in the ratio = 3: 2
Milk = (80/5) * 3 = 48 litres, Water = (80/5) * 2 = 32 litres
Given,
48/(32 + x) = 1/1
48 = 32 + x
x = 48 – 32 = 16 litres
25) Answer: C
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
26) Answer: B
Milk = 60 * 4/5 = 48 liters
Water = 60 * 1/5 = 12 liters
Milk in 20 liters = 20 * 4/5 = 16 liters
Water in 20 liters = 20 * 1/5 = 4 liters
(48 – 16 + x)/(12 – 4) = 5/1
40 = 32 + x
x = 8 liters
27) Answer: D
Milk = 5/8 * 64 = 40 liters
Water – 3/8 * 64 = 24 liters
(40 – 5x/8) / (24 – 3x/8 + x) = 25/39
(320 – 5x) * 39 = 25 * (192 + 5x)
12480 – 195x = 4800 + 125x
320x = 7680
x = 24 liters
28) Answer: C
CP of mixture = (67.5 *100)/125 = Rs. 54
= > 2 : 1
Total kg of variety 1 rice = 25 * 2 = 50 kg
29) Answer: B
Milk in 80 litres = 11/20 * 80 = 44 litres
Water in 80 litres = 9/20 * 80 = 36 litres
Milk in 40 litres = 11/20 * 40 = 22 litres
Water in 40 litres = 9/20 * 40 = 18 litres
(44 – 22 + 8)/(36 – 18 + x) = 1/1
30 = 18 + x
x = 12 litres
30) Answer: D
Milk in 36 liters = 36 * 5/9 = 20 liters
Water in 36 liters = 36 * 4/9 = 16 liters
(5x – 20)/(4x – 16 + 10) = 5/6
20x – 30 = 30x – 120
10x = 90
x = 9 liters
Total quantity = 9 * 9 = 81 liters
31) The vessel has 30 liters of mixture of milk and water in the ratio of 2:1. If 12 liters of mixture is replaced by water, then what is the ratio of the quantity of milk to water in the final mixture?
A.1:2
B.2:3
C.3:4
D.4:5
E.1:1
32) 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?
A.1:2
B.3:4
C.5:6
D.7:8
E.None of these
33) 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?
A.35:31
B.28:21
C.49:41
D.77:71
E.None of these
34) In what ratio must two varieties of rice worth Rs. 30 per kg and Rs. 40 per kg so that selling the rice Rs. 51 per kg he may gain 50%?
A.3: 2
B.1: 2
C.3: 4
D.4: 7
E.3: 5
35) A milkman has the mixture of milk and water in the ratio 5: 3 and then he added 20 liters of the water, then the ratio of the milk and water becomes 15: 19. What is the initial quantity of water in the mixture?
A.12 liters
B.15 liters
C.18 liters
D.21 liters
E.None of these
36) 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 approximately what percent of the quantity of the water in the final mixture?
A.33.33%
B.44.44%
C.66.66%
D.77.77%
E.22.22%
37) The 80 liters of mixture contains 40% of Petrol and 60% of Kerosene. In how much liters of Petrol added to the mixture, if the percentage of the kerosene in the mixture becomes 40%?
A.30 liters
B.40 liters
C.20 liters
D.50 liters
E.None of these
38) Jar contains 60 liters of milk and water in the ratio of 2:1. x liters of mixture is taken out and then 10 liters of the milk is added to the remaining mixture. Now the ratio of milk to water becomes is 11:4, then find the value of x?
A.15
B.20
C.30
D.25
E.None of these
39) A Jar contains 90 litres of the mixture of milk and water in the ratio of 5: 4 and 45 litres of the mixture is taken out. Then added x liters of the water in the remaining mixture, the ratio of the milk and water becomes 2: 3. Find the value of x?
A.18
B.17.5
C.16
D.15.5
E.14.5
40) A Jar contains 5x litres of the mixture of milk and water in the ratio of 3: 2 and 20 litres of the mixture is taken out. Then added 24 litres of the water in the remaining mixture, the ratio of the milk and water becomes 1: 2. Find the value of x?
A.15
B.10
C.20
D.30
E.None of these
Answers :
31) Answer: B
Milk in the vessel=2/3 * 30=20 liters
Water in vessel=1/3 * 30=10 liters
Milk in 12 liters of mixture=12 * 2/3=8 liters
Water in 12 liters of mixture=12 * 1/3=4 liters
Required ratio=(20 – 8):(10 – 4 + 12)
=12:18
=2:3
32) Answer: D
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
33) Answer: C
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
34) Answer: A
CP of the mixture = 51/150 * 100 = 34
The required ratio = 3: 2
35) Answer: C
5x/(3x + 20) = 15/19
45x + 300 = 95x
50x = 300
x = 6 liters
Initial quantity of the water = 3 * 6 = 18 liters
36) Answer: C
Milk = 2/3 * 60 = 40
Water = 1/3 * 60 = 20
Milk in 24 liter = 2/3 * 24 = 16
Water in 24 liter = 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%
37) Answer: B
Petrol = 40/100 * 80 = 32
Kerosene = 60/100 * 80 = 48
(32 + x)/48 = 60/40
2 * (32 + x) = 48 * 3
64 + 2x = 144
x = 40 liters
38) Answer: B
Milk in Jar A = 60 * 2/3 = 40 liters
Water in Jar A = 60 * 1/3 = 20 liters
Milk in x liter = x * 2/3
Water in x liter = x * 1/3
(40 – 2x/3 + 10) / 20 – x/3 = 11/4
(120 – 2x + 30) / (60 – x) = 11/4
660 – 11x = 600 – 8x
3x = 60
x = 20 liters
39) Answer: B
Milk = 5/9 * 90 = 50 litres
Water = 4/9 * 36 = 40 litres
Milk in 45 litres = 5/9 * 45 = 25 litres
Water in 18 litres = 4/9 * 45 = 20 litres
(50 – 25)/(40 – 20 + x) = 2/3
40 + 2x = 75
2x = 35
x = 17.5 litres
40) Answer: B
Milk in 20 litres = 3/5 * 20 = 12 litres
Water in 20 litres = 2/5 * 20 = 8 litres
(3x – 12)/(2x – 8 + 24) = 1/2
2x + 16 = 6x – 24
4x = 40
x = 10 litres
This post was last modified on September 21, 2023 5:47 pm