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A person gives $25\%$ discount on M.P and still gains $20\%$.How much percent is M.P above the C.P?

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Given:-

25% discount on MP

$0.75*MP = SP$ ------------ (i)

and

20% gain/profit on CP.

$1.2*CP = SP$ ..................... (ii)

Using eqn (i) and (ii)

$0.75*MP = 1.2*CP$

$MP = \frac{1.2}{0.75}*CP$

$MP = 1.6*CP$

which means MP is 60% above to CP.
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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.             $[\dfrac{1}{5} = 20\%]$

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