Question

What must be subtracted from each of the numbers 5, 7 and 10, so that the
resulting numbers are in continued proportion?

Answer 1

Let x be the number subtracted from 5, 7 and 10 so that
5 -x, 7 - x and 10 - x are is continued proportion. 
`[ 5 - x ]/[ 7 - x ] = [ 7- x ]/[ 10 - x ]`
⇒ ( 5 - x ) ( 10 - x ) = ( 7 - x )²
⇒ 50 - 15x + x² = 49 - 14x + x²
⇒ -15x + 14x = 49 -50
⇒ x = l