Question

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

Answer 1

Let the number added be x.
∴ (16 + x) : (26 + x) :: (26 + x) (40 + x)
    16 +x = 26 +x
    26 + x 40 + x
    (162 + x)(40 + x) = (26 + x2 )
     640 + 16x + 40x + x2 = 676 + 52x + x2
     56x - 52x = 676 - 640
     4x = 36

       x = 9
Thus, the required number which should be added is 9.