Artificial intelligent assistant

Could you please help me solve this problem of profit and loss? > A shopkeeper changes the discount on marked price of an article from 35% to 15%. Find the change in profit percentage? It seems that the data is insufficient but answer was given something else. I couldn't' understand how it's possible. Please help me solve this problem.

Suppose the shopkeeper's cost was $C$. Then there are three sales prices to consider: $S_1$, the original price. $S_2$ the price after a $35\%$ discount. And $S_3$, the price after a $15\% $ discount. In each case we define $P_i$ to be the associated profit percentage : $P_i=\frac {S_i-C}{C}$. You are asked to compare $P_2$ and $P_3$.

We easily see that $S_2=.65\,S_1$ and $S_3=.85\,S_1$ whence we conclude that $$P_2=.65\frac {S_1}C-1\;\;\;\&\;\;\;P_3=.85\frac {S_1}C-1$$ It follows that $$P_3=.85\times \frac {P_2+1}{.65}-1=\frac {17}{13}P_2+\frac 4{13}$$

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