We all know that,
Marked Price is the price marked on the price tag.
Markup is the percentage by which Marked Price is higher than the Cost Price. Thus, Markup is a percentage increase.
So, Cost Price * multiplying factor of Marked Price = Marked Price ------------------- 1)
Whereas, Discount is given due to bargaining or sales promotion on the Marked Price. And it is a percentage decrease.
So, Marked Price * multiplying factor of Discount = Selling Price -------------------- 2)
From 1) & 2) we get ,
Cost Price * multiplying factor of Marked Price * multiplying factor of Discount = Selling Price
We know that, Selling Price = Cost price * multiplying factor of Profit or Loss
∴ Cost Price * multiplying factor of Marked Price * multiplying factor of Discount = Cost price * multiplying factor of Profit or Loss
Or, multiplying factor of Marked Price * multiplying factor of Discount = multiplying factor of Profit or Loss
Now moving on to the question
A person gives $25\%$ discount on MP and still gains $20\%$
So, multiplying factor of Discount = $\dfrac{3}{4}$ & multiplying factor of profit = $\dfrac{6}{5}$
∴ Multiplying factor of Marked Price = $\dfrac{multiplying\hspace{0.1 cm} factor\hspace{0.1 cm} of\hspace{0.1 cm} profit}{multiplying\hspace{0.1 cm} factor\hspace{0.1 cm} of\hspace{0.1 cm} Discount}$
Multiplying factor of Marked Price = $\dfrac{6/5}{3/4} = \dfrac{6}{5}* \dfrac{4}{3} = \dfrac{8}{5} = (1+ \dfrac{3}{5})$
∴ Marked Price is increased by $\dfrac{3}{5}\% = (20*3)\% = 60\%$ from the Cost Price. $[\dfrac{1}{5} = 20\%]$