Question

If p varies as q and if p=5 when q=10, find q when p=20.

Answer 1

Hint: The phrase “p varies as q” in the above questions means the ratio of p and q is constant i.e., p, and q are proportional.

Complete step-by-step answer:

Let us first know what a ratio is.
A ratios is a quantity used to define a comparison between two quantities. A bit toward the advanced side, it is the quantity that defines how many times of one quantity is that of others.
At our level, apart from the definition, we will treat it as a simple fraction that defines a relation between two given quantities.
Now, starting with the solution to the above question. The phrase “p varies as q” in the above questions means the ratio of p and q is constant i.e., p, and q are proportional. Therefore we can write this mathematically as:
$\dfrac{p}{q}=\text{c}$
So, for the initial case, we get
$\dfrac{5}{10}=\text{c}$
Now for the case when p=20, we get
$\dfrac{20}{{{q}_{new}}}=\text{c}$
We will substitute the value of c from the previous result. On doing so, we get
$\dfrac{20}{{{q}_{new}}}=\dfrac{5}{10}$
On cross-multiplication, we get
$200=5q$
$\Rightarrow q=40$
Therefore, the value of q will be equal to 40 when p is equal to 20.

Note: Read the question carefully as in the question, including ratio, there is always a chance that the question might have a twist hidden in the words of the question, as we saw in the above question that the word ‘ratio’ was not directly mentioned but was solved using the concept of ratio.