Question

What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the resultant numbers are in proportion ?

• A. 4
• B. 3
• C. 6
• D. 7

Answer 1

Answer:

C. 6

Consider x to be the number to be subtracted from each term So, 23–x, 30–x, 57–x and 78–x are proportional

(23–x) : (30–x) :: (57–x) : (78–x)

$\frac{23-x}{30 - x} = \frac{57-x}{78-x}$

(23–x)(78–x) = (30–x)(57–x)

$23\times 78 - 23x -78x + x^2 = 30\times 57 - 30x - 57x + x^2$

1794 -101x = 1710 - 87x

101x - 87x = 1794 - 1710

14x = 84

x = 6