Whilst revising, a problem caught my eye and I cannot seem to find an answer. I am usually bad at these types of questions.
On a certain Russian-American committee, $\frac23$ of members are men, and $\frac38$ of the men are Americans. If $\frac35$ of the committee members are Russians, what fraction of the members are American women?
A. $\frac{3}{20}$ B. $\frac{11}{60}$ C. $\frac{1}{4}$ D. $\frac{2}{5}$ E. $\frac{5}{12}$
Could you please explain how to approach and analyse the problem, maybe give some hints or the complete procedure of solving?
I get a bit confused with all those fractions. What I tried was to convert them to percentages but that seemed a bad idea.
Sorry if this question is annoying.
Thank you.
Update: I solved the problem both intuitively and mathematically. Thanks.