# PROBLEM LINK:

Div1, Div2Practice

**Author:**Praveen Dhinwa

**Tester:**Triveni Mahatha

**Editorialist:**Adarsh Kumar

# DIFFICULTY:

Easy# PREREQUISITES:

None# PROBLEM:

You are given the initial price $p$ of a product. You need to first increase the price of this recipe by $x\%$ (from $p$) and then offer a discount of $x\%$. You need to compute the loss which occured to you as a result of this process, for $N$ items.# EXPLANATION:

Original price of the product = $p$.Chef decides to increase the price of recipe by $x\%$ which means new price = $p.\left(1+\frac{x}{100}\right)$.

Now he is going to offer a discount of $x\%$ on this price. Hence,

Final price = $p.\left(1+\frac{x}{100}\right).\left(1-\frac{x}{100}\right)$

$\Rightarrow$ Final price = $p.\left(1-\left(\frac{x}{100}\right) ^2\right)$

Since, the final price is less than original price:

Loss = Original price - final price

$\Rightarrow$ Loss = $p - p.\left(1-\left(\frac{x}{100}\right) ^2\right)$

$\Rightarrow$ Loss = $p.\left(\frac{x}{100}\right) ^2$

Coming back to original problem, we can use the formula for loss computed above to find loss for each recipe individually. Hence,

Answer = $\sum \limits_{i=1}^N ext{quantity$_i$}. ext{price$_i$}.\left(\frac{ ext{discount$_i$}}{100}\right) ^2$