What portion of work is done alone by students of a class?

Question

The teacher said , the work can be done alone or in a group . So students can make group to do the work . $\frac{2}{3}$th portion of male students and $\frac{3}{5}$th portion of female students done the work in group . So what portion of work is done alone by students of a class ?

My trying :

I have understood that this problem can be solved using vann diagram concept . But I cant understand how the concept of vann diagram should be applied here ?

Answer 1

Let $b$ the proportion of boys in the class, so $1-b$ i the proportion of girls (this is where Venn diagram helps).

We have that:

$\frac{2}{3}b + \frac{3}{5}(1-b)$ is the opposite of the proportion you are looking for. Simplifying a bit:

$\frac{1}{15}b + \frac{9}{15}$

The proportion of students, not working in group is:

$1 - (\frac{1}{15}b + \frac{9}{15}) = \frac{6}{15} - \frac{1}{15}b$

Doing some further assumption like the proportion of boys and girls is the same, so $b=\frac{1}{2}$. We can say the the proportion of students working in group is:

$\frac{1}{15}\frac{1}{2} + \frac{9}{15} = \frac{19}{30}$

And of course the proportion of students not working in group, supposing there is the same number of boys and girls, would be $1-\frac{19}{30} = \frac{11}{30}$

Answer 2

This question seems to be missing information, and thus has no solution without additional clarification. My advice what to do when facing questions such as this one:

• Try really hard to see if the missing information is there, just buried in the words. (In this problem, I don't believe it is.)
• Don't think it is your fault, that you "suck at maths" etc. Teachers are fallible like all humans, and information may well be genuinely missing.
• Convince yourself, by building examples where you supply the missing information, that the problem really is not solvable without this information.

For example, with 3 boys and 5 girls, you will have 1 boy and 2 girls working alone, which is 3/8 of the total. With 6 boys and 5 girls, you have 2 boys and 2 girls working alone, which is 4/11 of the total. Obviously, $3/8\ne 4/11$.

• Finally, throw the problem back to whoever gave it to you and ask for clarification. If they are reasonable, they will help; if not, it's again not your fault.