Question

In the year $2001$, the price of article $A$ is $20\% $ more than the price of article $B$. In the year $2002$, the price of article $A$ is $50\% $ more than the price of article $B$. From $2001$ to $2002$, if the price of $A$ has increased by $50\% $, by what percent has the price of $B$ increased?

Answer 1

Hint: Here in this question we know the pricing conditions of $A$. So, we can make equations from these conditions.
And then we will assume the price of article $B$ and by that we can get the price of article $A$ then by putting that into the equations we will get our answer.

Complete step-by-step answer:
First of in this question we know that
We have two articles $A$ and $B$.
So, let us assume that in the year $2001$
Price of article $B = x$
$ \Rightarrow $ As it is given that in the year $2001$, the price of article $A$ is $20\% $ more than the price of article $B$.
 So, Price of article $A = x + \dfrac{{20}}{{100}}\left( x \right)$
$ \Rightarrow $The price of $A = x\left( {1 + 0.2} \right)$
$ \Rightarrow $The price of $A = 1.2x$ ………………..(i)
And now, let us assume that in the year $2002$
Price of article $B = y$
$ \Rightarrow $As it is given that in the year $2002$, the price of article $A$ is $50\% $ more than the price of article $B$.
So, Price of article $A = y + \dfrac{{50}}{{100}}\left( y \right)$
$ \Rightarrow $The price of $A = y\left( {1 + 0.5} \right)$
$ \Rightarrow $The price of $A = 1.5y$ ………………..(ii)
Now, as it is given in the question that from $2001$ to $2002$, if the price of $A$ has increased by $50\% $
So, The price of $A$ in year $2002 = $ $\left( {1 + \dfrac{{50}}{{100}}} \right) \times $ The price of $A$ in year $2001$
$
   \Rightarrow 1.5y = \left( {1 + 0.5} \right) \times 1.2x \\
   \Rightarrow 1.5y = 1.5 \times 1.2x \\
   \Rightarrow y = 1.2x \\
 $
So, from here we can see that $y = 1.2x$
Now, we can find the percentage of price increase of articles from $2001$ to $2002$ because now we know the price of $B$ in both years.
So, percentage of price increased of article from $2001$ to $2002 = \dfrac{{P\left( {2002} \right) - P\left( {2001} \right)}}{{P\left( {2001} \right)}} \times 100$
Where, $P\left( {2002} \right) = $Price of article $B$ in $2002$and $P\left( {2001} \right) = $Price of article $B$ in $2001$
So, as founded above we know that, $P\left( {2002} \right) = 1.2x$ and $P\left( {2001} \right) = x$

$ \Rightarrow $The price of article $B$ is increased by $20\%$ from $2001$ to $2002$.

Note: In these types of questions the formation of the correct equation is very necessary, because students generally get confused while forming the equations. So, try to make an equation of that quantity who’s all conditions are known which is the article $A$ in this case. We use linear equations in one variable if only one quantity is to be found and we use linear equations in two variables if two unknown variables need to be found.