Question

What number should be subtracted from 28, 20, 37 and 26 so that the numbers formed are in proportion?

Answer 1

Answer:

Consider x be subtracted from each term

So, 23–x,30–x,57–x and 78–x are proportional

It can be written as

(23–x):(30–x)::(57–x):(78–x)

(30–x)

(23–x)

=

(78–x)

(57–x)

By cross multiplication

(23–x)(78–x)=(30–x)(57–x)

By further calculation

1794–23x–78x+x

2

=1710–30x–57x+x

2

⇒x

2

–101x+1794–x

2

+87x–1710=0

So we get

–14x+84=0

⇒14x=84

⇒x=

14

84

=6

Therefore, 6 is the number to be subtracted from each of the numbers.