Sets involving fractions

Question

A number of tourists were interviewed on their choice of means of travel. 2 thirds said that they traveled by road, 13/30 by air and 4/15 by both air and road.

How many tourists were interviewed?

How many traveled by air only?

Answer 1

2/3 - 4/15 = 10/15 - 4/15 = 6/15 = 2/5 travel by road only

13/30 - 4/15 = 13/30 - 8/30 = 5/30 = 1/6 travel by air only

note that 2/5 + 1/6 + 4/15 = 12/30 + 5/30 + 8/30 = 25/30 = 5/6

so 1/6 of it is missing