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)