[Math] Relation between ratio and percentage

Question

I would like to know easiest method to solve following:

Que:

If $p$ is $128$% of $r$, $q$ is $96$% of $r$ and $r$ is $250$% of $s$, find the ratio of $p$:$q$:$s$.

My Approach:

Step 1:

$p =\frac{128r}{100}$

$q = \frac{96r}{100}$

$r = \frac{250s}{100}$

So, $s = \frac{100r}{250}$

I do not know what to do further.
I know the answer but don't know how to achieve Ans: $16$:$12$:$5$

Thank You!

Answer 1

You have:

• $\frac{p}{r}=\frac{128}{100}$
• $\frac{q}{r}=\frac{ 96}{100}$
• $\frac{s}{r}=\frac{100}{250}$

Adjust them to the same denominator:

• $\frac{p}{r}=\frac{128}{100}\times\frac55=\frac{640}{500}$
• $\frac{q}{r}=\frac{ 96}{100}\times\frac55=\frac{480}{500}$
• $\frac{s}{r}=\frac{100}{250}\times\frac22=\frac{200}{500}$

And you get $p:q:s=640:480:200$.

Divide each factor by their greatest common divisor ($40$).

And you get $p:q:s=640/40:480/40:200/40=16:12:5$.