₹820 is divided among 6 men, 8 women and 12 boys in such a way that every woman gets an amount equal to that received by one man and one boy combined and that every man gets one and a half times the amount received by a boy. What is the total amount received by 8 women?

Given that,

Total number of 6 men, 8 women and 12 boys are getting a total of 820 Rs.

Let the boy is getting x Rs.

As per the given condition in the question,

So man will get $$=\dfrac{3}{2}x$$ Rs

So, women will get $$=x+\dfrac{3}{2}x =\dfrac{5}{2}x$$

Hence,

$$\Rightarrow 8\times \dfrac{5}{2}x+6\times \dfrac{3}{2}x+x\times 12=820$$

$$\Rightarrow \dfrac{40}{2}x+\dfrac{18}{2}x+x\times 12=820$$

$$\Rightarrow \dfrac{40+18+24}{2}x=820$$

$$\Rightarrow \dfrac{82}{2}x=820$$

$$\Rightarrow x=20$$Rs.

Hence the amount received by 8 women $$\Rightarrow 8\times \dfrac{5}{2}x=8\times \dfrac{5}{2}\times 20=400$$ Rs.