Question

A hawker gains the selling price of \[4\] gel pens on selling \[1\] dozen pens. What is his gain percentage?
A.\[40\% \]
B.\[50\% \]
C.\[55\% \]
D.\[60\% \]

Answer 1

Hint: For solving such problems, we should calculate selling price and cost price. We will use Gain percentage \[ = \dfrac{{Profit \times 100}}{{cost Price}}\]


Complete step by step solution:
We are given that hawker gains the selling price of \[4\]gel pens on selling \[1\]dozen pens.
\[ = {\text{ }}Selling{\text{ }}price{\text{ }}of{\text{ }}12{\text{ }}gel{\text{ }}pens{\text{ }}-{\text{ }}Cost{\text{ }}price{\text{ }}of{\text{ }}12{\text{ }}gel{\text{ }}pens\]
\[ = {\text{ }}Selling{\text{ }}price{\text{ }}of{\text{ }}4{\text{ }}gel{\text{ }}pens{\text{ }}\left( {it{\text{ }}is{\text{ }}gain{\text{ }}in{\text{ }}terms{\text{ }}of{\text{ }}S.P} \right)\]
So, let the S.P. of \[1\]gel pen \[ = {\text{ }}Rs{\text{ }}1\]
Then, according to question:
C.P. of \[12\]gel pens \[ = {\text{ }}Rs{\text{ }}8\]
S.P. of \[12\]gel pens \[ = {\text{ }}Rs{\text{ }}12\]
Therefore Gain \[\begin{array}{*{20}{l}}
  { = {\text{ }}S.P{\text{ }}-{\text{ }}C.P{\text{ }} = {\text{ }}Rs.{\text{ }}\left( {12{\text{ }} - 8} \right){\text{ }} = {\text{ }}Rs{\text{ }}4} \\
  {Gain{\text{ }}\% {\text{ }} = }
\end{array}\]
\[ = \dfrac{{Profit \times 100}}{{costPrice}}\]
$
   = \dfrac{4}{8} \times 100 \\
   = 50\% \\
 $
Therefore, the correct option is B


Note: As we are given the gains in terms of selling price, thus, we will calculate the gain first using C.P and S.P. And then the gain percentage.