Question

$Rs3500$ 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?

Answer 1

Let $x,y$ and $z$ be the amounts received by the first, second and the third person, respectively.
We have: $x=50\%$ of $y$
$=\frac{50}{100}\times y$
$=\frac{1}{2}\times y$
$\therefore y=2x$
Again, $y=50\%$ of $z$
$\Rightarrow y=\frac{1}{2}\times z$
$\Rightarrow z=2y$
$\Rightarrow z=2\times \left(2x\right)$
Thus, $z=4x$
According to the question,
$x+y+z=3500$
Substituting the values of $z$ and $y$, we get
$\Rightarrow x+2x+4x=3500$
$\Rightarrow 7x=3500$
$\therefore x=500$
Thus, $y=2x=2\times 500=1000$
and $z=4x=4\times 500=2000$
Thus, the amounts received by the first, second and the third person are $Rs500,Rs1000$ and $Rs2000$, respectively.