Alligations or Mixtures
Aptitude

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Q.

How many kgs of Basmati rice costing Rs.42/kg should a shopkeeper mix with 25 kgs of ordinary rice costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?

 A.

20.0 kgs

 B.

12.5 kgs

 C.

16.0 kgs

 D.

200.0 kgs

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Solution:
Option(A) is correct

As the trader makes 25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture = Rs.32/kg. 

Step 2:
C.P of  1 kg of rice of  1st kind = Rs. 42

C.P of  1 kg of rice of  2nd kind = Rs. 24

Mean price = Rs. 40

By the rule of Alligation, we have:

C.P. of 1kg of                    C.P. of 1kg of

rice of 1st                          rice of 2nd

kind (Rs. 42)                      kind (Rs. 24)

 

                    \                    /

                     Mean Price
                         (Rs. 32)

                   /                    \

 

       40 - 24          :            42 - 32  

          (8)                              (10)

Let the amount of Basmati rice being mixed be $x$ kgs.

\begin{align*} 
8:10 & =x:25\\ 
\left(\dfrac{4}{5}\right) & =\left(\dfrac{x}{25}\right)\\ 
\Rightarrow x &=20 \text{ Kgs.} 
\end{align*}

Alternatively:

Let the amount of Basmati rice being mixed be $x$ kgs.

As the trader makes 25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture = Rs.32/kg. 

i.e. $(x \times 42)+(25 \times 24)=32(x+25)$

⇒ $42x+600=32x+800$

⇒ $10x=200$ 

⇒ $x=20 kgs.$


(1) Comment(s)


Pankaj Sharma
 ()

NOTE:

1:Take profit %age = 20

=>CP=32 and Correct Answer = 20 kgs

2:Take profit %age = 25

=>CP=30 and Correct Answer = 12.5 kgs.