Alligations or Mixtures
Aptitude

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Q.

In what ratio must a person mix three kinds 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?

 A.

11 : 77 : 7

 B.

25 : 45 : 8

 C.

27 : 23 : 6

 D.

11 : 45 : 7

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Solution:
Option(A) is correct

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

                    C.P of 1 Kg                        C.P of 1 Kg

                    Wheat of 1st                 wheat of 3rd

                    kind (120p)                    kind (174p)

 

                                  \                             /

                                       Mean Price

                                          (141p)

                                  /                             \

 

                            33                                    21

By Alligation rule:

$\dfrac{\text{Quantity of 1st kind of wheat}}{\text{Quantity of 3rd kind of wheat}} = \dfrac{33}{21}=\dfrac{11}{7}$

So they must be mixed in the ratio $11 : 7$

Step 2: 

Mix wheat of 1st kind and 2nd kind to obtain a mixture worth of Rs. 1.41per Kg

                    C.P of 1 Kg                        C.P of 1 Kg

                    Wheat of 1st                 wheat of 3rd

                    kind (120p)                    kind (144p)

 

                                  \                             /

                                       Mean Price

                                          (141p)

                                  /                             \

 

                            3                                     21

By alligation rule:

$\dfrac{\text{Quantity of 1st kind of wheat}}{\text{Quantity of 2nd kind of wheat}}=\dfrac{3}{21}=\dfrac{1}{7}$
So they must be mixed in the ratio 1 : 7

Thus,
\begin{align*}
&\dfrac{\text{Quantity of 2nd kind of wheat}}{\text{Quantity of 3rd kind of wheat}}=\\
&\left(\dfrac{\text{Quantity of 1st kind of wheat}}{\text{Quantity of 3rd kind of wheat}}\right)\times \left(\dfrac{\text{Quantity of 2nd kind of wheat}}{\text{Quantity of 1st kind of wheat}}\right)\\
& \Rightarrow \dfrac{\text{Quantity of 2nd kind of wheat}}{\text{Quantity of 3rd kind of wheat}}=\left(\dfrac{11}{7}\times \dfrac{7}{1}\right) =\left(\dfrac{11}{1}\right)
\end{align*} 

Thus, Quantities of wheat of $1^{st} : 2^{nd} : 3^{rd} = 11 : 77 : 7$

Edit: For a different and shortcut approach, check Murugan's comment.


(12) Comment(s)


Current
 ()

Best way to solve these types are -

Considering x,y,z the three wheat breeds with 1.2 rs/kg , 1.44rs/kg, 1.74rs/kg respectively. Finding pairs which can give the given mean price of 1.41 . Only two pairs (1.2,1.44) (1.2,1.74) . Applying alligation in both cases x:y=0.03:0.21

x:z=0.33:0.21

Thus x:y:z= (0.03+0.33:0.21:0.21)

So 36:21:21

12:7:7 is only possibility



Rajesh Kumar
 ()

can any one tell me why we use 120 two times .. not 144 confused !!


Shivam
 ()

Hi Rajesh,

In order to get avg. 1.41 we need to have values such that 1.41 lies between them. We can not use a combination 1.44 and 1.74 to get 1.41. Hence two possible alligations will be 1.2 and 1.44 , 1.2 and 1.74. And every time while paring to solve alligation we have to take care of it.


Rajesh Kumar
 ()

#rajesh

can any one tell me why we use 120 two times to mix but not 144 ..confused !!



Anuj Bhawsar
 ()

why are we do we add the ratio

c:a:b=7:(11+1):7.

Simple way is to get by substitution and ans comes as 11 : 77 : 7.



Prince
 ()

Alligation has failed this question.

Correct answer: Multiple ratios possible

One possibility =12:7:7


Abhishek Jain
 ()

this is the only possibility. 11 : 77 : 7 is wrong


Murugan
 ()

$a:b=1:7$

$a:c=11:7$

$c:a:b=c:a::a:b$

So,

$c:a:b=7:11::7:1$

To find out the value of $a$,

$=(7*1):(7*11)::(7*11):(1*11)$

Therefore,

$=7:77::77:11$

$a:b:c=11:77:7$



Sachin Dahiya
 ()

Approach for this question and the last 2 question is different and also the answer shown as correct is not matching the given information. it should be 12:7:7 #Sachin



Naresh
 ()

$c:a=7:11$

a:b=1:7

So

$c:a:b=7:(11+1):7$

means,

$a:b:c = 12:7:7$

is the correct answer Smile


Dudeja
 ()

I agree with Naresh.
the correct answer is 12:7:7

mean average= 12*120 +7*144 + 7*174 /26 equals to 141. Otherwise, also answer is calculated adding the ratio.A: C 11:7
A : B 7:7
12 : 7 : 7

Sonal
 ()

There are multiple answers possible in such ratio questions. But I guess challenge is to follow an approach that matches the given options.