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1) Jar A contains 50 liters of mixture of milk and water in the ratio of 3:2 and Jar B contains n liters of mixture of milk and water in the ratio of 2:1. If both mixtures are mixed, then the ratio of milk to water becomes 5:3. Find the value of n?
A.75
B.30
C.90
D.150
E.None of these
2) A vessel contains a mixture of milk and water in the ratio of 7:1 respectively. If 24 liters of mixture is taken out and 19 liters of water added to the remaining mixture, then the quantity of milk in the final mixture is 29 liters more than that of water. Find the initial quantity of milk in the mixture?
A.45 liters
B.63 liters
C.36 liters
D.72 liters
E.None of these
3) A vessel contains milk and water in the ratio of 2:1. If 15 liters of mixture is taken out and replaced with water, then the ratio of milk and water becomes 7:5, then find the total quantity of mixture initially?
A.90 liters
B.120 liters
C.60 liters
D.150 liters
E.None of these
4) A vessel contains 150 litres of pure wine. 30 litres of wine is taken out and replaced with the same amount of water and the process is repeated for one more time. Find the difference between the initial and final quantity of wine.
A.45 litres
B.35 litres
C.54 litres
D.25 litres
E.None of these
5) A milkman has the mixture of milk and water in the ratio of 5: 3. If he sold 16 liters of the mixture and replaced with same quantity of water, 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
6) A shopkeeper bought 32 kg of variety 1 rice for Rs.45 per kg and also bought 40 kg of variety 2 rice for Rs.54 per kg. He mixed both varieties and sold them at a profit of x%. If the selling price of the mixture is Rs.56 per kg, then find the value of x?
A.18
B.20
C.25
D.12
E.None of these
7) In a mixture of milk and water, the quantity of milk is (x+40) and water 40 L. If 20 L milk and 8 L water is added to the mixture, then the ratio of milk and water becomes 5:3. Find the x% of initial water in the mixture?
A.7
B.5
C.12
D.16
E.None of these
8) A vessel contains 100 liters mixture of water and acid in the ratio of 2:3. If 25% of the mixture is taken out and 5 liters of acid is added to the mixture, then the quantity of water left in the vessel is what percentage of the quantity of acid left in that vessel?
A.60%
B.50%
C.45%
D.75%
E.None of these
9) Ratio of milk to water in a mixture is 3:2. 30 Liters of mixture taken out and then 20 Liters of water is added in the mixture. Now the ratio of milk to water of the mixture is 3:7. If X% of the total initial mixture is 14, then find the value of X?
A.28
B.15
C.32
D.36
E.56
10) Ana bought 50 kg of rice at Rs.78 per kg and 25 kg of rice at Rs.96 per kg. If she mixed them, then the mixture is sold at a profit of 25%. Find the selling price of the mixture per kg.
A.Rs.80
B.Rs.90
C.Rs.70
D.Rs.105
E.None of these
Answers :
1) Answer: B
The milk in the jar A = 50 * 3/(3 + 2) = 50 * 3/5 = 30 liters
The water in the jar A = 50 – 30 = 20 liters
(30 + 2x)/(20 + 1x) = 5/3
90 + 6x = 100 + 5x
x = 10
n = (2 + 1) * 10 = 3 * 10 = 30
2) Answer: E
Let the quantity of milk in the initial mixture=7x
And the quantity of water in the initial mixture=1x
The quantity of milk in the final mixture=7x-24*7/8=7x-21
The quantity of water in the final mixture=1x-24*1/8+19=1x+16
(7x-21)-(x+16)=29
7x-21=x+16+29
6x=66
x=11
Required value=7*11=77 liters
3) Answer: B
Milk in the initial mixture=2x
Water in the initial mixture=x
(2x-15*2/3)/(x-15*1/3+15)=7/5
(2x-10)/(x+10)=7/5
10x-50=7x+70
3x=120
x=40
Required total=(2+1)*40=120 liters
4) Answer: C
Final quantity of wine = 150 * (1 – 30/150)2 = 150 * 16/25 = 96 litres
Required difference = 150 – 96 = 54 litres
5) 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
6) Answer: D
32 * 45 + 40 * 54 = (32 + 40) * 56 * 100/(100 + x)
1440 + 2160 = 72 * 56 * 100/(100 + x)
3600 = 72 * 56 * 100/(100 + x)
112 = 100 + x
x = 12
7) Answer: E
So, we can say, [x+40+20]/(40+8) = 5/3
Or, 3x+180=48*5=240
Or, 3x=60, or, x=60/3=20
Required value = 40*20/100=8 L
8) Answer: A
Let the quantity of acid in the vessel initially = 100 * 3/(3 + 2) = 100 * 3/5 = 60 liters
And the quantity of water in the vessel initially = 100 – 60 = 40 liters
25% of the quantity of mixture in the vessel = 100 * 25/100 = 100/4 = 25 liters
The ratio of the quantity of acid to water in the vessel finally = (60 – 25 * 3/(3 + 2) + 5) : (40 – 25 * 2/(3 + 2))
= (60 – 15 + 5) : (40 – 10)
= 50:30
= 5:3
Required percentage = 3/5 * 100 = 60%
9) Answer: A
Let milk and water is 3a and a.
So, [3a-(30*3/5)]/[2a-(30*2/5)+20] = 3/7
3a-18/ (2a+8) =3/7
6a + 24 = 21a – 126
15a = 150
a = 10
Total mixture is 5*10=50
So, X% of 50 = 14, so X=14*100/50=28
10) Answer: D
The cost price of mixture per kg = (50 * 78 + 25 * 96)/(50 + 25) = (3900 + 2400)/75 = 6300/75 =Rs.84
The selling price of mixture per kg = 84 * 125/100 = Rs.105
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