Any person desiring to engage or work at the business of plumbing, either as a master plumber, employing plumber, or as a journeyman plumber, in cities having a population of fifteen thousand or more, shall make application to a board of examiners herein provided for, and shall at such times and places as said board may designate, be compelled to pass such examination as to his qualifications as said board may direct. Said examination may be made in whole or in part in writing and shall be of practical and elementary character, but sufficiently strict to test the qualifications of the applicant.