Alligations or Mixtures

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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?


Rs. 147.50


Rs. 785.50


Rs. 175.50


Rs. 258.50

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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.

(3) Comment(s)


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


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 $\textbf{175.50}$.


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

this is alternate solution and time saving also.