# Moderate Alligations or Mixtures Solved QuestionAptitude Discussion

 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

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.

## (7) Comment(s)

()

what if 1st two elements aren't mixed in equal proportion?

SHRINWANTU RAHA
()

1 st kind:

126*1/4=31.50

2nd kind

135*1/4=33.75

Let price of the third is x rs./kg.

2/4kg worth of 1/2x rs.

so, 31.50+33.75+x/2=153

x= 175.50

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

Shree
()

BECAUSE OF THE RATIO OF DISTRIBUTION