Question

What number must be subtracted from each of the numbers $10,12,19,24$ to get the numbers which are in proportion?

Answer 1

Suppose that $x$ is the number that is to be subtracted.
Then, $(10-x):(12-x)::(19-x):(24-x)$

Now ,we know that, Product of extremes $=$ Product of means

$\Rightarrow (10-x)\times (24-x)=(12-x)\times (19-x)$

$\Rightarrow 240-10x-24x+x^2=228-12x-19x+x^2$

$\Rightarrow 240-34x=228-31x$

$\Rightarrow 3x=12$

$\therefore x=4$
.
Hence, $4$ must be subtracted from each of the numbers $10,12,19$ and $24$ to get the numbers which are in proportion.