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1) 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
2) A vessel has 180 litres of the mixture of petrol and kerosene in the ratio of 5:4. If x litres of the mixture is taken out and then added 40 litres of petrol and 26 litres of kerosene. If the final ratio of the petrol and kerosene is 4:3, then find the value of x?
A.27
B.30
C.36
D.45
E.None of these
3) 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 quantity of water in the final mixture.
A.65.61 litres
B.64.59 litres
C.16.69 litres
D.24.39 litres
E.58.24 litres
4) Vessel A contains the mixture of milk and water in the ratio of 4:1 and the vessel B contains the mixture of milk and water in the ratio of 3:4. If both vessels mixtures are mixed, what is the ratio of the milk and water in the final mixture?
A.37:23
B.41:25
C.43:27
D.45:29
E.None of these
5) A milkman has 60 liters mixture of milk and water in the ratio of 3:2 and then he sold 20 liters of the mixture. Then the milk man added x liters of water, now the ratio of the water and milk becomes 7:6. Find the value of x?
A.10
B.12
C.14
D.15
E.None of these
6) A mixture contains the milk and water in the ratio of 4: 3. If 16 liters of the milk is taken out and 13 liters of the water is added to that mixture, the ratio of milk and water becomes 1: 2. What is the initial quantity of water?
A.48 liters
B.36 liters
C.30 liters
D.27 liters
E.None of these
7) 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
8) 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 added 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
B.12
C.14
D.16
E.None of these
9) The mixture of 350 litres contains milk and water in the ratio of 4 : 3. How much quantity of water should be added to the mixture to get 40 % milk in it?
A.80 liters
B.150 liters
C.100 liters
D.120 liters
E.None of these
10) 80 litres of a mixture of milk and water contains 24 litres more milk than water, then find the ratio of milk to water in the new mixture, if 10 litres of water is added to it?
A.26: 19
B.24: 17
C.32: 21
D.37: 25
E.None of these
Answers :
1) 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
2) Answer: C
Petrol in 180 litres = 5/9 * 180 = 100
Kerosene in 180 litres = 4/9 * 180 = 80
(100 – 5x/9 + 40)/(80 – 4x/9 + 26) = 4/3
(900 – 5x + 360) * 3 = 4 * (720 – 4x + 234)
3780 – 15x = 3816 – 16x
x = 36 litres
3) Answer: D
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
4) Answer: C
Milk in vessel A = 4/5
Water in vessel A = 1/5
Milk in vessel B = 3/7
Water in vessel A = 4/7
Required ratio = (4/5 + 3/7):(1/5 + 4/7)
=43:27
5) Answer: B
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
(36 – 12)/(24 – 8 + x) = 6/7
96 + 6x = 168
6x = 72
x = 12 liters
6) Answer: D
(4x – 16)/(3x + 13) = ½
3x + 13 = 8x – 32
5x = 45
x = 9 liters
Initial quantity of the Water = 3 * 9 = 27 liters
7) 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%
8) 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
9) Answer: B
Let the water should be added is x,
Total quantity of mixture = 350 litres
Ratio of milk and water = 4 : 3
Total quantity of milk = 200 litres
Total quantity of water = 150 litres
Given,
(200 / (150 + x)) = (40 / 60)
300 = 150 + x
x = 150
Required water = 150 liters
10) Answer: A
Total mixture = 80 litres
M + W = 80 —> (1)
Milk = Water + 24
M – W = 24 —> (2)
By solving the equation (1) and (2), we get,
M = 52 litres, W = 28 litres
The ratio of milk to water in the new mixture
= > 52: (28 + 10)
= > 52: 38 = 26: 19
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