To solve this puzzle, you can use the following steps:
Take the monkey first and leave the tiger and the bananas on the starting side.
Leave the monkey on the opposite side and return to the starting side alone.
Take the tiger to the opposite side and leave it there. Pick up the monkey and bring it back to the starting side.
Leave the monkey on the starting side and pick up the bananas. Bring them to the opposite side and leave them with the tiger.
Return to the starting side alone and pick up the monkey, bringing it to the opposite side where the tiger and bananas are waiting.