Question

If \[{\text{CP}}\]of 20 articles is the same as ${\text{SP}}$of $x$articles. If the profit is $25{\raise0.5ex\hbox{$\scriptstyle \bullet $}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle \bullet $}}$ , the value of $x$is
$
  {\text{A}}{\text{. 15}} \\
  {\text{B}}{\text{. 16}} \\
  {\text{C}}{\text{. 18}} \\
  {\text{D}}{\text{. 25}} \\
    \\
$

Answer 1

Hint:- In this question first you need to find out the CP by letting it to the $x$ and SP, profit in terms of $x$. Then using profit (Profit = $\dfrac{{{\text{SP}}}}{{{\text{CP}}}} \times 100$) formula and equate it to the $25{\raise0.5ex\hbox{$\scriptstyle \bullet $}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle \bullet $}}$ to get the value of $x$.

Complete step by step answer:
Cost Price(CP): The price, at which an article is purchased, is called its cost price(CP).
Selling Price(SP): The price, at which an article is sold is called its selling price(SP).
Profit: If SP is greater than CP the seller is said to have profit
 $ \Rightarrow $Profit= SP-CP ${\text{eq}}.1$
Let CP of each article be Rs. 1
 CP of $x$ articles = Rs.$x$
SP of $x$ articles = Rs. 20 {$\therefore $Given}
Then,
Profit= Rs{$\therefore $ from eq.1}
And Profit = $25{\raise0.5ex\hbox{$\scriptstyle \bullet $}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle \bullet $}}$ {$\therefore $Given}
Since, Profit = $\dfrac{{{\text{SP}}}}{{{\text{CP}}}} \times 100$
Therefore,
$
   \Rightarrow {\text{ }}\dfrac{{20 - x}}{x} \times 100 = 25 \\
   \Rightarrow {\text{ }}2000 - 100x = 25x \\
   \Rightarrow {\text{ }}125x = 2000 \\
   \Rightarrow {\text{ }}x = 16 \\
 $
Hence, the option ${\text{B}}{\text{.}}$ is correct.

Note:-Whenever you get this type of question the key concept of solving this is to assume the CP or SP which is known, equal to $x$.Then find the different values in terms of variables. And try to find out that known variable because by knowing, you can get your answer.