# $4$ kg of rice at  $5$ per kg is mixed with $8$ kg of rice at  $6$ per kg. Find the average price of the mixture. [closed]

$$4$$ kg of rice at ' $$5$$ per kg is mixed with $$8$$ kg of rice at ` $$6$$ per kg. Find the average price of the mixture. Then, by the unitary method:

$$n_1 + n_2$$ corresponds to $$A_2 – A_1$$

$$\rightarrow 1 + 2$$ corresponds to $$6 – 5$$

That is, $$3$$ corresponds to $$1$$

$$\therefore n_2$$ will correspond to $$\dfrac{(A_2 - A_1)n_2}{(n_1 +n_2 )}$$

In this case $$\frac{1}{3} \cdot 2 = 0.66$$. Hence, the required answer is $$5.66$$.

My doubt is that I don't understand this solution given in my book, I'm stuck at how $$n_2$$ will correspond to $$\dfrac{(A_2 - A_1)n_2}{n_1 + n_2}$$.

PS: Here $$A_2$$ and $$A_1$$ are $$6$$ and $$5$$, I will attach the reference If you don't understand the terminologies, This is a basic question in Alligation and Mixture.

## 1 Answer

Let Rice A cost \$$$5/$$kg and Rice B cost \$$$6/$$kg

$$4$$kg of Rice A will cost you $$4\times 5=\20$$

$$8$$kg of Rice A will cost you $$8\times 6=\48$$

There will be no difference of you buying $$4$$kg of type A and $$8$$kg of type B separately compared to you buying them as a mixture. Either way, you end of spending $$\68$$ for $$4+8=12$$kg of hybrid rice. Hence, we get

Average price $$=\frac{\68}{12kg}=\5.67/$$kg

I would suggest you refrain from using a textbook formula for such questions as this is not a general result. Also, IMO there is much more value in understanding how to solve the question and being able to derive the formula if needed.