My solution was very naive:
Let $N = 100$. Then, $M = 150$. Then, $$\frac{N}{N+M}= \frac{100}{100+150}= 0.40$$ which corresponds to $40\%$. Therefore $N$ corresponds to $40\%$ of $M + N$.
I think the solutions is wrong. I need help to find my mistake. Please help me.
The final answer that $N$ is $40\%$ of $M+N$ is correct.
If the answer was marked wrong, then I can ony imagine it was because you assumed that $N=100$. However this trick will always give the right answer. You could prove it without assuming anything about $N$ in the following manner.
Since $M$ is $150\%$ of $N$ it follows that $M = 1.5N$ so that
$$ \frac{N}{M+N} = \frac{N}{1.5N+N} = \frac{N}{2.5N} = \frac{1}{2.5} = 0.4$$