A profit of 20% is made on the goods when a discount of 10% is given on the list price. If a discount of 20% is allowed on the list price, the profit to be made will be
$
  (A)\,6\% \\
  (B)6\dfrac{2}{3}\% \\
  (C)3\dfrac{1}{3}\% \\
  (D)4\dfrac{2}{3}\% \\
$

Hint: Consider marked price as $100$ and apply conditions. First, we have to consider the market price as 100 and find the S.P, from which we are going to find it to equal with the 90% of L.P. We will be able to find the L.P, then after that we will be able to find the new selling price of the value. Then, from the new selling price, we will subtract it from the marked price and then we will find the gain.

Complete step by step solution:
First, let us consider the marked price as $Rs.\,100$, then in the question we are given that the profit is made is \[20\% \]n which means its selling price is $Rs.120$, this value is obtained when a discount of \[10\% \] is applied on the list price, so it means that
\[90\% {\text{ }}of\;L.P = Rs120\]
From, this we can find the value of L.P
From which we get
\[
  \Rightarrow L.P = 120 \times \dfrac{{100}}{{90}} \\
  \Rightarrow L.P = \dfrac{{400}}{3} \\
\], i
So, it’s asked that when a discount of \[20\% \] is applied what will the profit be made
New $S.P = 80\% \,\,of\,\dfrac{{400}}{3} = \dfrac{{320}}{3}$
We have found the new selling price, to find the gain/profit, we will subtract it from the original selling price.
$
  \Rightarrow Gain = \dfrac{{320}}{3} - 100 \\
   \Rightarrow 6\dfrac{2}{3}\% \\
 $

Hence the correct answer is option ‘B’.

Note: Since, we have no initial value that is why we have to consider the marked price as 100, such that we can have further calculations easily and also, we have to read the question well, because we have to form an expression which gets us the final profit value.