# Difficult Alligations or Mixtures Solved QuestionAptitude Discussion

 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

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.