Question

What number must be subtracted from each of the numbers $13,17,34,42$ so that the resulting four numbers are in proportion?

Answer 1

Let the number to be subtracted be $x$

Since after subtrction they will all be in proportion

$\Rightarrow \frac{13-x}{17-x}=\frac{34-x}{42-x}$

Cross multiplying

$\Rightarrow (13-x)(42-x)=(34-x)(17-x)$

$\Rightarrow 13(42-x)-x(42-x)=34(17-x)-x(17-x)$

$\Rightarrow 546-13x-42x+x^2=578-34x-17x+x^2$

Rearranging the terms

$\Rightarrow 546-55x=578-51x$

$\Rightarrow -55x+51x=578-546$

$\Rightarrow -4x=32$

$\Rightarrow x=-\frac{32}{4}$

$\Rightarrow x=-8$

So $-8$ should be subtracted for the numbers to be in proportion.