Question

There are $9$ coins in a bag, $5$ of which are sovereigns and the rest are unknown coins of equal value; find what they must be if the probable value of a draw is $12$ shillings.

Answer 1

$1sovereign=20shillings$

Let the value of the other coin be $xshillings$

If coin drawn is sovereign then probable value $=\frac{5}{9}\times 20=\frac{100}{9}$

If other coin is drawn then probable value $=\frac{4}{9}\times x=\frac{4x}{9}$

Total probable value $=12$

$\Rightarrow \frac{100}{9}+\frac{4x}{9}=12\Rightarrow 100+4x=108\Rightarrow 4x=8\Rightarrow x=2$

So the coins are of value $2shilling$ each