Question

What least number of must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion ?

Answer 1

Let the number subtracted be x.
so
$(7-x):(17-x)::(17-x):(47-x)$
$\to (7-x)/(17-x)=(17-x)/(47-x)$

$\to (7-x)(47-x)=(17-x{)}^2$

$\to 329-47x-7x+x^2=289-34x+x^2$

$\to 329-289=34x+54x$

$\to 20x=40$

$\to x=2$

Thus, the required number which should be subtracted is 2.