How to find Profit percent in this case?

Question

A trader allows a discount of 20% on his goods and still makes a profit of 25%.Find the profit percent made, if he sells his goods at: (1) the Marker price (2) at 10% discount

What i've tried:

let MP = 100
D=20%
=> SP = 80

SP = 80
P = 25%

SP      CP
125     100
80       ?

CP = (80 * 100)/125
   = 64

profit = SP - CP 
       = 80 - 64
       = 16

P% = 16/64 * 100  
   = 25%  

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but the correct answer is 56.25 %

Answer 1

Let $S$ be the usual sale price, $C$ be the cost.

You are given that $\frac{0.8 S } { C} = 1.25$.

For (1), you want to compute $\frac{S } { C} = \frac{1} {0.8} \frac{0.8 S } { C} = \frac{1} { 0.8} 1.25 = 1.5625$ (ie, 56.25%).

For (2), you want to compute $\frac{0.9 S } { C} = 0.9 \cdot 1.5625 = 1.40625$ (ie, 40.625%).