APTITUDE-ALLIGATION OR MIXTURES COMPLEX PROBLEMS

Complex Problems:

1.Tea worth Rs 126 per Kg are mixed with a third variety in the ratio 1:1:2. If the mixture is worth Rs 153 per Kg , the price of the third variety per Kg will be?

Solution:
Since First and second varieties are mixed in equal proportions
so their average price =Rs (126+135)/2 = 130.50.

So the mixture is formed by mixing two varieties ,one at
Rs 130.50 per Kg and the other at say Rs x per Kg in the
ratio 2:2 i e,1:1 we have to find x.

Cost of 1Kg tea of 1st kind RS 130.50 Cost of 1Kg tea of 2n d kind Rs x.

Mean Price Rs 153

x-153 22.50

(x=153)/22.5 = 1 =>x-153 = 22.5
x = 175.50.
Price of the third variety =Rs 175.50 per Kg.

2.The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?

Solution:Let the C.P of milk be Re 1 per liter.
Milk in 1 liter mixture of A = 4/7 liter.
Milk in 1 liter mixture of B = 2/5 liter.
Milk in 1 liter mixture of C = 1/2 liter.
C.P of 1 liter mixture in A=Re 4/7
C.P of 1 liter mixture in B=Re 2/5.
Mean Price = Re 1/2.
By rule of allegation we have:

C.P of 1 liter mixture in A C.P of 1 liter mixture in B
4/7 2/5

Mean Price ½

1/10 1/14

Required ratio = 1/10 : 1/14 = 7:5.

3.How many Kg s of wheat costing him Rs 1.20,Rs 1.44 and Rs 1.74 per Kg so that the mixture may be worth Rs 1.41 per Kg?

Solution:
Step1:Mix wheat of first and third kind to get a mixture
worth Rs 1.41 per Kg.

C.P of 1 Kg wheat of 1st kind 120p C.P of 1 Kg wheat of 3rd kind 174p

Mean Price 141p

33 21

They must be mixed in the ratio =33:21 = 11:7

Step2:Mix wheats of 1st and 2n d kind to obtain a mixture
worth of 1.41.per Kg.

C.P of 1 Kg wheat of 1st kind 120p C.P of 1 Kg wheat of 2n d kind 144p

Mean Price 141p

3 21

They must be mixed in the ratio = 3:21=1:7.

Thus,Quantity of 2n d kind of wheat / Quantity of 3rd kind of wheat = 7/1*11/7= 11/1
Quantities of wheat of 1st :2n d:3rd = 11:77:7.


4.Two vessels A and B contain spirit and water mixed in the ratio 5:2 and 7:6 respectively. Find the ratio n which these mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ratio 8:5?

Solution:Let the C.P of spirit be Re 1 per liter.
Spirit in 1 liter mix of A = 5/7 liter.
C.P of 1 liter mix in A =5/7.
Spirit in 1 liter mix of B = 7/13 liter.
C.P of 1 liter mix in B =7/13.
Spirit in 1 liter mix of C = 8/13 liter.
C.P of 1 liter mix in C =8/13.

C.P of 1 liter mixture in A 5/7 C.P of 1 liter mixture in B 7/13

Mean Price 8/13

1/13 9/91

Therefore required ratio = 1/13 : 9/91 = 7:9.

5.A milk vendor has 2 cans of milk .The first contains 5% water
and the rest milk. The second contains 50% water. How much milk
should he mix from each of the container so as to get 12 liters
of milk such that the ratio of water to milk is 3:5?

Solution:Let cost of 1 liter milk be Re 1.
Milk in 1 liter mixture in 1st can = 3/4 lit.
C.P of 1 liter mixture in 1st can =Re 3/4
Milk in 1 liter mixture in 2n d can = 1/2 lit.
C.P of 1 liter mixture in 2n d can =Re 1/2
Milk in 1 liter final mixture = 5/8 lit.
Mean Price = Re 5/8.

C.P of 1 lt mix in 1st Re3/4 C.P of 1 lt mix in 2nd Re1/2

Mean Price 5/8

1/8 1/8

There ratio of two mixtures =1/8 :1/8 = 1:1.
So,quantity of mixture taken from each can=1/2*12
= 6 liters.

6.One quantity of wheat at Rs 9.30 per Kg are mixed with another quality at a certain rate in the ratio 8:7. If the mixture so formed be worth Rs 10 per Kg ,what is the rate per Kg of the second quality of wheat?

Solution:Let the rate of second quality be Rs x per Kg.

C.P of 1Kg wheat of 1st 980p C.P of 1 Kg wheat of 2nd 100x p

Mean Price 1000p

100x-1000p 70 p

(100x-1000) / 70 = 8/7
700x -7000 = 560
700x = 7560 =>x = Rs 10.80.
Therefore the rate of second quality is Rs10.80

7.8lit are drawn from a wine and is then filled with water. This operation is performed three more times.The ratio of the quantity of wine now left in cask to that of the water is 16:81. How much wine did the cask hold originally?

Solution:
Let the quantity of the wine in the cask originally be x liters.
Then quantity of wine left in cask after
4 operations = x(1- 8/x)4lit.
Therefore x((1-(8/x))4)/x = 16/81.
(1- 8/x)4=(2/3) 4
(x- 8)/x=2/3
3x-24 =2x
x=24.

8.A can contains a mixture of two liquids A and B in the ratio 7:5 when 9 liters of mixture are drawn off and the can is filled with B,the ratio of A and B becomes 7:9. How many liters of liquid A was contained by the can initially?

Solution:
Suppose the can initially contains 7x and 5x liters
of mixtures A and B respectively .
Quantity of A in mixture left = (7x- (7/12)*9 )lit
= 7x – (21/4) liters.
Quantity of B in mixture left = 5x – 5/12*9
= 5x – (15/4) liters

Therefore (7x – 21/4)/ (5x – 15/4+9)=7/9
(28x-21)/(20x +21)= 7/9
(252x -189)= 140x +147
112x = 336
=> x=3.
So the can contains 21 liters of A.

9.A vessel is filled with liquid,3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Solution:
Suppose the vessal initially contains 8 liters of liquid.
Let x liters of this liquid be replaced with water
then quantity of water in new mixture
= 3-(3x/8)+x liters.
Quantity of syrup in new mixture = 5 – 5x/8 liters.
Therefore 3 – 3x/8 +x = 5 – 5x/8
5x+24 = 40-5x
10x = 16.
x= 8/5.
So part of the mixture replaced = 8/5*1/8 =1/5.

If you have questions, please ask below

6 Comments


  1. karan says:

    A vessel contains a mixture of 24 litres of milk and 6 litres of water and second vessel contains a mixture of 15 litres of milk and 10 litres of water. How much mixture of milk and water should be taken from the first and the second vessel separately and kept in third vessel so that the third vessel may contain a mixture of 25 litre of milk and 10 litre of water?

  2. Mike says:

    Great job man….want some more

  3. pavithra says:

    A coffee seller has two types of coffee Brand A costing 5 bits per pound and
    Brand B costing 3 bits
    per pound. he mixes two brands to get a 40 pound mixture. he sold this at 6 bits
    per pound. the seller
    gets a profit of 33 1/2 percent. how much he has used Brand A in the mixture?

  4. pavithra says:

    any one sole dis

  5. pavithra says:

    can any one solve above problm

  6. sanjay says:

    there are 1000 wine’s bottle in party in 1 of them there is poison if any body drink’s it, he/she will die in 10 to 20 min and we have 24 hours to find the wine bottle in which there is poison?

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