## PROBLEM LINK:

**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 = $\sum \limits_{i=1}^N \text{quantity$_i$}.\text{price$_i$}.\left(\frac{\text{discount$_i$}}{100}\right) ^2$## Time Complexity:

O(N)