Are pushups alone enough for a toned body?

For a toned Upper body - Yes
Pushups are great but you need to do different variations of it to target different parts of the upper body.

Wide Grip Push Up

Close Grip Pushup/Diamond push Ups

Divebomber/Hindu Push Ups
Target-Chest,Triceps,Lower back and hamstrings

T-Push Ups
Target-Full Body

Two Feet Hops
Target- Chest and Core(This is a fat burner if done fast)

Side to Side/Alternative front back Push Ups
Target- Shoulders

Spiderman pushups, knee crosses
Target- Core

Target- Core

Develop a routine with these Pushups, maybe 10 each with 20 seconds rest followed by a 30 to 60 second plank,
and then gradually increase the no's or the better the sets.

Lower body doesn't ask for much, squats and calf raises will do just fine, unless you plan to compete professionally.
Same with back. you have to do pull type exercises not push type to target the back, so put in two variations of pull ups, wide and narrow grip.

All the best
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