Question

What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion?

Answer 1

Let x be added to each number then
16 + x, 26 + x and 40 + x
are in continued proportion.
⇒ ${\displaystyle \frac{16+x}{26+x}=\frac{26+x}{40+x}}$
Cross Multiplying
(16 + x) (40 + x) = (26 + x) (26 + x)
⇒ 640 + 16x + 40x + x² = 676 + 26x + 26x + x²
⇒ 640 + 56x + x² = 676 + 52x + x²
⇒ 56x + x² - 52x - x² = 676 - 640
⇒ 4x = 36
⇒ x = ${\displaystyle \frac{36}{4}}$ = 9
∴ 9 is to be added.