Final answer:
Zali initially had marbles in a 3:4 ratio compared to Muthu. After Muthu gave half of his marbles to Zali, the new ratio became 5:2 in favor of Zali.
Step-by-step explanation:
Let's call the number of marbles Zali had 3x and the number Muthu had 4x, where x is a common multiple representing the quantity of the marbles.
Initially, the ratio of the marbles Zali had to Muthu's was 3:4.
Muthu gave half of his marbles to Zali, so he gave away 2x marbles.
Now, Zali has 3x + 2x = 5x and Muthu has 4x - 2x = 2x.
Therefore, the new ratio of the number of marbles Zali had to Muthu's is 5:2.