This wonderful set is a word problems based set and literally stands out from the rest due to its involment of linear equations. In this question, you are required to find the maxima with the given conditions and data. How about solving this question and cracking your CAT preparation online? Yes! Let's do it. Dive into this CAT previous year paper question and nail it!
An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.
Question 3 : What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?
Wonderful question. Let us first outline the overall variables.
500x + 200y + 100z = 5000. Or, 5x + 2y + z = 50.
If the preferred denomination is 500, we know that x > (y + z).
If the preferred denomination is 200, we know that y > (x + z).
If the preferred denomination is 100, we know that z > (y + x).
After this, we are off to the questions.
To start with, we want to have the maximum number of customers who can be serviced with the available Rs. 500 notes. In other words, we need to figure out the minimum number of Rs. 500 notes with which one customer can be serviced.
In other words, can we give a customer only one Rs. 500 note and meet all conditions.
1 Rs. 500 note gives us Rs. 500. The remaining Rs. 4500 needs to delivered with Rs. 200 and Rs. 100 notes.
The best case scenario of 22 Rs. 200 and one Rs. 100 note, we have a total of 24 notes which is not possible.
With 2 Rs. 500 notes, we would have RS. 1000. 20 Rs. 200 notes make it 22 in total. Not possible again.
With 3 Rs. 500 notes, we would have RS. 1500. 17 Rs. 200 notes and one Rs. 100 note make it 21 in total. Not possible again.
With 4 Rs. 500 notes and 15 Rs. 200 notes, our conditions are met. So, the best case scenario involves 4 Rs. 500 notes.
So, with each customer being given 4 notes, we can service a maximum of 12 notes.
The question is "What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?"
Choice C is the correct answer.
CAT® (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.
2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093