Test: Alligation & Mixture- 2 - CAT MCQ

The buying price is :
100/110 × 68.20 = 62
Let the amount of tea worth rs 60 be x and the amount of tea worth rs 65 be y
The total amount is : x + y
60x + 65y = 62(x + y)
60x + 65y = 62x + 62y
65y - 62y = 62x - 60x
3y = 2x
3/2 = x / y
3 : 2

Let initially vessel have 8 l of liquid and x lof this liquid be replaced with water then quantity of water in new

Let the sugar sold at 8% gain = x
Therefore, Sugar sold at 18% gain = (1000 - x)
Let CP of sugar = Rs.y per kg
Total CP = Rs.100y
Therefore,
(108/100 * xy) + 118/100(1000-x)y
114/100*1000y
= 108xy + 118000y - 118xy = 114000y
10x = 4000
x = 400
Quantity sold at 18% profit
= 1000 - 400 = 600 kg

Let C.P. of 1 litre milk be Re. 1
Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.
C.P. of 1 litre mixture = Re.(100/125 * 1) = 4/5
By the rule of alligation, we have

Ratio of milk to water = 4/5 : 1/5
=> 4:5
Hence, percentage of water in the mixture = 1/5 x 100%    
= 20%

Let C.P. of 1 litre milk be Rs. 1
S.P. of 1 litre of mixture = Rs. 1, Gain = 
∴ C.P. of 1 litre of mixture = 
BY the rule of alligation, we have:

∴ Ration of water and milk = 

The ratio of milk and water in Bottle 1 is 7:2 and the ratio of milk and water in Bottle 2 is 9:4
Therefore, the proportion of milk in Bottle 1 is 7/9 and the proportion of milk in Bottle 2 is 9/13
Let the ratio in which they should be mixed be equal to X:1.
Hence, the total volume of milk is 7x/9 + 9/13
The total volume of water is 2X/9 = 4/13
They are in the ratio 3:1
Hence,
Therefore, 91X + 81 = 78X + 108
Therefore X = 27/13

The proportion of water in the first mixture is 1/3
The proportion of Liquid A in the first mixture is 2/3
The proportion of water in the second mixture is 1/4
The proportion of Liquid B in the second mixture is 3/4
The proportion of water in the third mixture is 1/5
The proportion of Liquid C in the third mixture is 4/5
As they are mixed in the ratio 4:3:2, the final amount of water is

The final amount of Liquid A in the mixture is 4 x 2/3 = 8/3
The final amount of Liquid B in the mixture is 3 x 3/4 = 9/4
The final amount of Liquid C in the mixture is 2 x 4/5 = 8/5
Hence, the ratio of Water : A : B : C in the final mixture is

From the given choices, only option C  is correct.

The selling price of the mixture is Rs.40/kg.
Let a be the price of 1 kg of tea A in the mixture and b be the price per kg of tea B.
It has been given that the profit is 10% if the 2 varieties are mixed in the ratio 3:2
Let the cost price of the mixture be x.
It has been given that 1.1x = 40
x = 40/1.1
Price per kg of the mixture in ratio 3:2 = 

3.3a + 2.2b = 200 --- (1)
The profit is 5% if the 2 varieties are mixed in the ratio 2:3.
Price per kg of the mixture in ratio 2:3 = 

2.1a+ 3.15b = 200 -- (2)
Equating (1) and (2), we get,
3.3a+2.2b = 2.1a + 3.15b
1.2a = 0.95b