AGENTCHEF - Editorial

editorial
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PROBLEM LINK:

Practice
Contest: Division 1
Contest: Division 2
Contest: Division 3
Contest: Division 4

Author: notsoloud
Tester: mridulahi
Editorialist: iceknight1093

DIFFICULTY:

732

PREREQUISITES:

None

PROBLEM:

Chef gets a 20\% commission on selling an insurance policy, each of which costs X dollars.
Find the minimum number of sales he needs to make, to earn at least 100 dollars.

EXPLANATION:

20\% of X can be written as 0.2X, that is, each sale earns Chef 0.2X dollars.

So, if Chef makes K sales, he’d earn 0.2X\cdot K dollars.
We want the smallest K such that this is at least 100.
Working it out,

0.2X\cdot K \geq 100 \\ X\cdot K \geq \frac{100}{0.2} = 500 \\ K\geq \frac{500}{X}

Hence, we want K\geq \frac{500}{X}.

K must be an integer, so the smallest one we can choose is K = \left\lceil \frac{500}{X} \right\rceil.
Here, \left\lceil \ \right\rceil denotes the ceiling function.

TIME COMPLEXITY

\mathcal{O}(1) per testcase.

CODE:

Editorialist's code (Python) 
for _ in range(int(input())):
    x = int(input())
    print((500 + x - 1)//x)