Question

The three scales below are perfectly balanced if $\bullet =3$. What are the values of $\Delta$ and $\ast ?$

Answer 1

It has been given that $\bullet =\mathrm{3....}\left(1\right)$

$\left(a\right)5\ast =2\Delta +2\bullet ....\left(2\right)$

$\left(b\right)2\Delta =2\ast +2\bullet ...\left(3\right)$

$\left(c\right)3\ast +3\bullet =3\Delta \Rightarrow \ast +\bullet =\Delta ...\left(4\right)$

By putting equation $\left(4\right)$ in $\left(2\right)$ we get

$5\ast =2(\ast +\bullet )+2\bullet$

$\Rightarrow 3\ast =4\bullet$

$\Rightarrow 3\ast =4\times 3\cdots \cdots \left[\text{from}\right(1\left)\right]$

$\Rightarrow \ast =4$

Putting these values in equation $\left(4\right)$ we get

$\ast +\bullet =4+3=\Delta$

$\Rightarrow \Delta =7$

$\therefore \Delta =7\&\ast =4$