Question:
Rs 3500 is to be shared among three people so that the first person gets 50% of the second, who in turn gets 50% of the third. How much will each of them get?
Solution:
Let $x, y$ and $z$ be the amounts received by the first, second and the third person, respectively.
We have :
$x=50 \%$ of $y$
$=\frac{50}{100} y=\frac{1}{2} y$
$\therefore y=2 x$
Again, $y=50 \%$ of $z$
$=\frac{1}{2} z$
$\therefore z=2 y$
$=2(2 x)$
$=4 x$
Also, $x+y+z=3500$
Substituting the values of $z$ and $y$, we get:
$x+2 x+4 x=3500$
$\Rightarrow 7 x=3500$
$\Rightarrow x=500$
$\therefore y=2 x=2(500)$
$=1000$
$\therefore z=4 x=4(500)$
$=2000$
Thus, the amounts received by the first, second and the third person are Rs 500, Rs 1000 and Rs 2000 , respectively.