In an examination, the number of those who passed and the number of those who failed were in the ratio 3 : 1. Had 8 more appeared, and 6 less passed, the ratio of passed to failures would have been 2 : 1. Find the number of candidates who appeared.

What number must be added to each of the number 4, 6, 8, 11 in order to make them proportional ?

If 2, 6, p, 54 and q are in continued proportion, find the values of p and q.

If a, b, c, d, e are in continued proportion, prove that a : e = a⁴ : b⁴.