# Ratio between kinds of fish in the aquarium

In a big aquarium there are three kinds of fish:$A,B,C$.In the last year the ratio between the number of fish of kind $A$ to the number of fish of kind $B$ has increased by $\cfrac{50}{100}$. Furthermore the ratio between the number of $B$ (read fish of kind $B$) to the number of $C$ has increased by $\cfrac{20}{100}$. By how much has incresed the ratio between $A/C$ ?

$a)\cfrac {35}{100} \space\space\space,\space\space\space b)\cfrac{70}{100} ,\space\space\space c)\cfrac{80}{100} ,\space\space\space d)\cfrac{100}{100}$

What I've tried

It's given that $\cfrac{A}{B}=r$ where this is the ratio before the last year ,where nothing has changed.

so I have that the new ratio is $\cfrac{A'}{B'}=r+\cfrac{50}{100}r=\cfrac{150}{100} r$

The same reasoning goes for $B/C=s$ and the new ratio is $\cfrac{ B'}{C'}=s+\cfrac{20}{100}s=\cfrac{120}{100}s$

So in order to get the desired ratio $\cfrac{A'}{C'}$ I just multiply the previous two ratios $$\cfrac{A'}{B'}\cdot \cfrac{B'}{C'}=\cfrac{150}{100} r \cdot \cfrac{120}{100}s=\cfrac{150 \cdot 120}{100^{2}}rs=\cfrac{180}{100}rs$$

My answer is none of the options given,but my logic looks right (I think).

What am I doing wrong ?

• Subtract $rs$ from the result you have got Dec 29, 2015 at 8:58

There is nothing wrong with your calculations.

It is correct that $\cfrac{A'}{C'} = \cfrac{18}{10}*\cfrac{A}{C}$.

But the question is asking you by how much this new ratio differs from the previous ratio (i.e. $\cfrac{A'}{C'} - \cfrac{A}{C}$) which is just $\cfrac{18}{10}*\cfrac{A}{C} - \cfrac{A}{C} = \cfrac{8}{10}*\cfrac{A}{C}$

You can see that the new ratio is 8/10 larger than the previous one, so the answer is $\cfrac{80}{100}$.

• Ahhh !Right,I simply overlooked that detail.Thank you ! Dec 29, 2015 at 9:47

$\dfrac{180}{100}rs$ is the new ratio of $\dfrac{A}{C}$. It's the old ration plus the increase.

To find the increase $x$, write $\dfrac{180}{100}rs = rs + xrs$.

Your approach is absolutely correct but incomplete.

The question asks for increase in value but you have found out the increased value.

So,just subtract the increased value from the original value to get the net increase.

So,$(\frac {180}{100}\times \frac AC)-\frac AC=\frac {80}{100}$

• @Mr.Y You are welcome!! Dec 29, 2015 at 12:46