A popular riddle about time is:
 
Q: What time is it when an elephant sits on a fence (car, chair, clock, watch, etc.)?
A: Time to get a new fence (car. chair, clock, watch, etc.).
 
This riddle was posted in many newspapers in the feature “Time for Fun—Puzzlers” by Bob Tippett on June 2, 1949:
 
Q: What time is it when an elephant sits on a fence?
A: Time to get a new fence.
   
     
2 June 1949, Wisconsin State Journal (Madison, WI), “Time for Fun—Puzzlers” by Bob Tippett, pg. 13, col. 7:
What time is it when an elephant sits on a fence?
Time to get a new fence.
   
31 August 1952, Boston (MA) Sunday Herald, “Good Sport Page,” pg. 24, col. 5:
Here are some riddles: What time is it when an elephant sits on your fence? (Answer: time to get it repaired)
(...)
JEAN BATCHELDER (11)
West Medford.
 
24 December 1955, The Afro-American (Baltimore, MD), “Riddles,” pg. 21, col. 3:
What time is it when an elephant sits on a fence?
Time to build another fence.
 
15 October 1958, Mansfield (OH) News-Journal, “Fun Time—The Riddle Box” by Arkady Leokum, pg. 35, col. 8:
What time is it when an elephant sits on a fence?
Time to get a new fence.
 
Google Books
Arithmeriddles
By Lowry Waring Harding
Columbus, OH: Association for the Study of Educology, Ohio State University
1961
Pg. 54:
Q. What time is it when an elephant sits on a fence?
A. Time to build a new fence.
       
Google Books
It’s about Time:
Creative Activities about Time
By Robynne Eagan and Tracey Ann Schofield
Carthage, IL: Teaching & Learning Co.
1997
Pg. 114:
Try your “timing” with the following jokes and lines:
 
What time is it when an elephant sits on your fence?
Time to get a new fence.
   
Twitter
cam_tortuga
@CameronLinville
What time is it when an elephant sits on your clock? Time to get a new clock
4:02 PM - 7 Mar 2012
 
Twitter
Awesome Daily Elephant Facts and Jokes
@AwesomeElephant
Q: What time is it when an elephant stands on your skateboard?
A: Time to get a new skateboard.
This awesome joke was sponsored by @benshapiro thank you Ben, very cool!
6:40 AM - 18 Sep 2018
       
Twitter 
Real Vegas
@realvegasdotcom
Replying to @kwilli1046
What time is it when an elephant sits on your car? Time to get a new car! We are Farmers, dum de dum de dum dum dum.
3:40 AM - 3 Jan 2019
 
Twitter
Don Faist
@FaistDon
Replying to @gypsysweetluv
What time is it when an elephant sits on your watch?
Time to get a new watch.
I love my dad jokes
10:27 AM - 15 Jan 2019
 
Twitter
Dev ✌🏻
@devhope71
“What time is it when an elephant sits on a chair?
Time to get a new chair “
-the banana laffy taffy I ate in Anna’s room yesterday
10:14 PM - 24 Jan 2019
 
Twitter
Baby Jesus
@JCautomatic
Follow Follow @JCautomatic
Wife: What time is it when an elephant sits on the fence?
Me: African or Indian.
Wife: Why does it matter?
Me: Because they live in different time zones obvs!
Wife: You really are an absolute fucking bureau aren’t you?
7:33 AM - 1 Feb 2019