If M is $150\%$ of $N$, then $N$ is what percent of $M + N$?

Question

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.

Why you think its wrong – Archis Welankar Dec 07 '15 at 16:47 — Archis Welankar, Dec 07 '15 at 16:47
It was a MCQ question and there is no 40% in answer – maruf Dec 07 '15 at 16:48 — maruf, Dec 07 '15 at 16:48
Is it $66.67%$ of m+n – Archis Welankar Dec 07 '15 at 16:52 — Archis Welankar, Dec 07 '15 at 16:52
@ArchisWelankar No, it is 40%. See answer below – Shailesh Dec 07 '15 at 16:57 — Shailesh, Dec 07 '15 at 16:57
What were the multiple choice options? – fleablood Dec 07 '15 at 18:28 — fleablood, Dec 07 '15 at 18:28

Jorik · Accepted Answer · 2015-12-07T16:59:05.163

2

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

$$ \frac{N}{M+N} = \frac{N}{1.5N+N} = \frac{N}{2.5N} = \frac{1}{2.5} = 0.4$$

edited Dec 07 '15 at 16:59

answered Dec 07 '15 at 16:51

Jorik

1,411

Beat me to it. Great illustration. – Pete Mancini Dec 07 '15 at 16:54

If M is $150\%$ of $N$, then $N$ is what percent of $M + N$?

1 Answers1