Alligations or Mixtures
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Q.

Three types of wheat of Rs. 1.27, Rs. 1.29 and Rs. 1.32 per kg are mixed together to be sold at Rs. 1.30 per kg. In what ratio should this wheat be mixed?

 A.

$1:2:3$

 B.

$1:1:2$

 C.

$2:1:3$

 D.

$2:2:3$

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Solution:
Option(B) is correct

Let's say three variety of whet are $w_1 (\text{ Rs. 1.27})$, $w_2 (\text{ Rs. 1.29})$ and $w_3 (\text{ Rs. 1.32})$.

We first deal with type of wheat of Rs. 1.27 $(w_1)$, Rs. 1.32.$(w_3)$ to get mean price Rs. 1.30

In order to make calculations easier we multiply every number by $100$. Since we are working on ratios, it won't finally change the answer.

Thus, wheat1 $(w_1)$ and wheat2 $(w_3)$ are in the ratio,

  $w_1$                 $w_3$
 127                 132
        \                 /
           mean
            130
         /                \
$(130-132)$    :   $(127-130)$
     $-2$                     $-3$

$\Rightarrow w_1 : w_3=2:3$

Now, lets take the wheat of Rs. 1.29 $(w_2)$, Rs. 1.32  $(w_3)$. to get mean price Rs. 1.30

 $w_2$                 $w_3$
 129                  132
        \                /
           mean
            130
         /                 \
$(130-132)$     :    $(129-130)$
     $-2$                      $-1$

$\Rightarrow w_2 : w_3=2:1$

Thus, final ratio,

$\Rightarrow w_1: w_2 : w_3=2:2:(3+1)$

$\Rightarrow w_1: w_2 : w_3=1:1:2$

Edit: Thank you Prashant for poining towards an error. Typos have been corrected.


(7) Comment(s)


Vikram Cavala
 ()

127x + 129y + 132z = 130(x+y+z)

2z = 3x + y

Now substituting the options will be quicker



VinothKumar
 ()

Weighted average can be used here.

Deviation of wheat prices from the mean are -3, -1, 2.

Deviation multiplied with the ratio gives zero.

-3x-y+2z = 0.

Using options, Option(3) is correct.



Sidharth
 ()

i have a doubt... as you said in the intro that "The cost price of a unit quantity of the mixture is called the mean price" but in the question Rs. 1.30 is the selling price. So, it means the selling price can also be considered as a mean price or not?



Anu
 ()

Solution is not updated yet ! I



Kshitij
 ()

w1:w3 = 2:3

w2:w3 = 2:1

then w1:w2 = w1/w3 * w3/w2 = 2/3 * 1/2 = 1/3

then w1:w2:w3 = 2:6:3

how is it 1:1:2?



Prashant
 ()

kindly check the answer


Deepak
 ()

Thank you Prashant for letting me know the anomaly. Solution is updated and should be okay now.