Alligations or Mixtures
Aptitude

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Q.

Teas worth Rs. 126 per kg and Rs. 135 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?

 A.

Rs. 147.50

 B.

Rs. 785.50

 C.

Rs. 175.50

 D.

Rs. 258.50

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Solution:
Option(C) is correct

Since first and second varieties are mixed in equal proportions.
So, their average price $= \text{Rs. } \left(\dfrac{126+135}{2}\right)$
$= \text{Rs. } 130.50$

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 $

By the rule of alligation, we have:

Cost of 1 kg                Cost of 1 kg

of 1st kind                 of 2nd kind

(Rs. 130.50)                  (Rs. $x$)

 

                \                      /

                   Mean Price

                                   (Rs. 153)

                 /                     \

 

       $x - 153$                       22.50

$\Rightarrow x-\dfrac{153}{22.50}=1$
$\Rightarrow x-153=22.50$
$\Rightarrow x=$ 175.50 Rs.

Edit: For a quicker approach, using the weighted average method, check comment by  Jaideep.


(4) Comment(s)


Kkpan
 ()

but if it is done by taking 1st and third ratio..then we will have to consider 1:1 ratio and then it will come as 180



Murali
 ()

if we assume third party as $x$,then we have to take $1:1:2$ for all to $153$. so $\dfrac{(135+126+2x)}{4} = 153$. solve it we will get easily $\textbf{175.50}$.



Jaideep
 ()

\(\dfrac{126+135+2x}{4} =153\)

this is alternate solution and time saving also.


Namita Kumari
 ()

Not able to understand why 4 came below?? I know 153 is mean value so it must come 3 becoz quantity is there