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51. In 80 litres mixture of milk and water the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ?

Discuss
Solution:
According to the question,
Milk : WaterInitial Ratio7×2:3×2Final Ratio2×7:1×7
∴ Remember water is added not milk, so make milk equal
M:WInitial14:6Final14:7) =20unit1
20 units = 80 litres1 unit = 4 litresWater added = 4 litres
52. 300 kg of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution ?

Discuss
Solution:
In 300 kg of solution,
Percentage of sugar = 40%
∴ Sugar = 300×40100   = 120 kg
Let x kg of sugar be added.
Now, according to the question
120+x300+x=12240+2x=300+x2xx=300240x=60kg
53. The milk and water in a mixture are in the ratio 7 : 5. When 15 litres of water are added to it. The ratio of milk and water in the new mixture becomes 7 : 8. The total quantity of water in the new mixture is -

Discuss
Solution:
According to the question,
Milk:Water
7:57:8)3unit
∴ Remember water is added and not milk, so make milk equal but here milk is already equal
3 units = 15 litres1 unit = 5 litres8 units = 40 litres
Total quantity of water in the new mixture = 40 litres
54. A gold smith has two qualities of gold, one of 12 carats and another of 16 carats purity. In what proportion should he mix both to make an ornament of 15 carats purity ?

Discuss
Solution:
According to the question,
By using alligation method :
Alligation mcq solution image
Ratio of quantity 1:3
55. 7 kg of tea costing Rs. 280 per kg is mixed with 9 kg of tea costing Rs. 240 per kg. The average price per kg of the mixed tea is ?

Discuss
Solution:
According to the question,
Average price of mixed tea
 = 280×7+240×916 = 1960+216016 = 412016 = Rs. 257.50
56. A mixture of a certain quantity of milk with 16 litres of water is worth 90 paise per litre. If pure milk be worth Rs. 1.80 per litre. How much milk is there in the mixture ?

Discuss
Solution:
Let the price of water = Rs. 0
According to the question,
Cost price of pure milk = Rs. 1.80
Cost price of the mixture = Rs. 0.90
Now using Alligation method.
Alligation mcq solution image
Therefore the amount of water is equal to the amount of Milk in mixture.i.e. 16 litter Milk in Given Mixture
57. Nikita bought 30 kg of wheat at the rate of Rs. 9.50 per kg and 40 kg of wheat at the rate of Rs. 8.50 per kg and mixed them. She sold the mixture at the rate of Rs. 8.90 per kg. Her total profit or loss in the transaction was -

Discuss
Solution:
According to the question,
Cost price of the mixture
= 30 × 9.50 + 40 × 8.50
= 285 + 340
= Rs. 625
Selling price of the mixture
= 8.90 × 70
= Rs. 623
Loss = Cost price - Selling price
Loss = 625 - 623 = Rs. 2
58. Three vessels whose capacities are in the ratio of 3 : 2 : 1 are completely filled with milk mixed with water. The ratio of milk and water in the mixture of vessels are 5 : 2, 4 : 1 and 4 : 1 respectively. Taking 13 of first, 12 of second and 17 of third mixture, a new mixture kept in a new vessel is prepared. The percentage of water in the new mixture is -

Discuss
Solution:
Capacities of vessels
3:2:1
M:WTMixtureV - 1(5:2=7)×5V - 2(4:1=5)×7V - 3(4:1=5)×7
Equate the mixture
M:WTMixture(V - 1)25:10=35(V - 2)28:7=35(V - 3)28:7=35
CapacitiesM:W=Total Mix.(V1)×375:30=105(V2)×256:14=70(V1)×128:7=35
Water taken out
13 of water in (V - 1)     +12 of water in (V - 2)     +17 of water in (V - 3)
13×30+12×14+17×710+7+118
Similarly mixture will be
13×105+12×70+17     × 35
⇒ 75
% of water = 1875×100=24%
59. In an alloy, zinc and copper are in the ratio 1 : 2. In the second alloy, the same elements are in the ratio 2 : 3. If these two alloys be mixed to form a new alloy in which two elements are in the ratio 5 : 8, the ratio of these two alloys in the new alloys is -

Discuss
Solution:
Let them be mixed in the ratio x : y
Then, in 1st alloy, Zinc = x3 and Copper = 2x3
2nd alloy, Zinc = 2y5 and Copper = 3y5
Now, we have
x3+2y5:2x3+3y5=5:8or,5x+6y10x+9y=58or,40x+48y=50x+45yor,10x=3yxy=310
Thus, the required ratio = 3 : 10

Alligation Method :
You must know that we can apply this rule over the fractional value of either zinc or copper.
Let us consider the fractional value of zinc.
Alligation mcq solution image
Therefore, they should be mixed in the ratio
=165:239or,165×392=310or,3:10
60. A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is -

Discuss
Solution:
Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x(3x+5)=4520x=4(3x+5)8x=20x=2.5
Quantity of alcohol
= (4 × 2.5) litres
= 10 litres.