Question

The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. If the average number of shoppers in the original store at any time was 45, then the average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time?
A. 60
B. 70
C. 80
D. 50

Answer 1

Hint: In this question Little’s law is used. We know that Little’s Law is a theorem that determines the average number of items in a stationary queuing system, based on the average waiting time of an item within a system and the average number of items arriving at the system per unit of time.

Complete step-by-step solution:
According to the original information given, we have the estimated average number of shoppers in the original store at any time (N) as 45.
In the question, it states that, in the new store, the manager estimates that an average of 90 shoppers per hour (60 minutes) enter the store. So, we can express it as $\dfrac{90}{60}$ , which on simplification gives us 1.5 shoppers per minute.
The manager also estimates that each shopper stays in the store for an average of 12 minutes.
So, now we have got average number of shoppers as r = 1.5 per minute and average waiting time as T = 12 minutes.
We will now apply the Little’s law. Thus, we have
N = rT
Substituting the values, we get
$\Rightarrow$ (1.5)(12)
On multiplying, we get that 18 shoppers will be present in the new store at any time.
So, we can get the percentage as
$\Rightarrow \dfrac{45-18}{45}\times 100$
$\Rightarrow$ 60 percent less than the average number of shoppers in the original store at any time.
So, the correct option is A i.e. 60.

Note: In this question, particularly the Little’s law is applied. This is the best approach for this question. Students should know how to find the percentage. There might be chances of mistakes in multiplication too. Students might take 90 as the original shop data instead of 45 and this will lead to them choosing option C. 80 as the correct answer.