Question

What number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion?

Answer 1

Let x be added to 5, 11, 19 and 37 to make them in proportion.
5 + x : 11 + x : : 19 + x : 37 + x
⇒ (5 + x) (37 + x) = (11 + x) (19 + x)
⇒ 185 + 5x + 37x + x² = 209 + 11x + 19x + x²
⇒ 185 + 42x + x² = 209 + 30x + x²
⇒ 42x - 30x + x² - x² = 209 - 185
⇒ 12x = 24
⇒ x = 2
∴ Least number to be added = 2.