# Find the original price if the price after reduction by $15\%$ and subsequent increase by $5\%$ is $1606.60$ euro

I want to solve the following examples. Solution is 1800 euro. I used this formula: $S=\frac{100 i}{p}$, but I couldn't get the result. Please help me. The example is:

The price of a product is reduced 15%, then the price is increased by 5%, and now the price is 1606.60 euro. Find the original price of the product.

Let $P$ the original price, $d=15\%$ the first reduction rate, $i=5\%$ the increaing rate and $S=1606.60$ the final price.
You have that $P$ is reducted to $P(1-d)=P'$ and then is increased to $P'(1+i)=S$; thus $$S=P(1-d)(1+i)\Longrightarrow P=\frac{S}{(1-d)(1+i)}=\frac{1606.60}{(0.85)(1.05)}=1800$$
• Except it's $1800.11$, not $1800$. @superboll, are you sure the final price is not meant to be $1606.50$? – TonyK Mar 7 '16 at 12:41
$$p$$ price $$(p-15p/100)$$ reduced by 15% $$(p-15p/100)5/100$$ increased by 5% $$(p-15p/100)+5(p-15p/100)/100=1606.5$$ $$20(p-3p/20)+(p-3p/20)=20\cdot1606.5$$ $$21\cdot(17p/20)=3213$$ $$p=\frac{20\cdot3213}{21\cdot17}=1800$$