CAT 2018 Slot 1 — DILR Question 23
Answer the following question based on the information given below.
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.
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?
Answer & solution
- A
13
12
- C
16
- D
10
Here we just need to keep in mind that
> the customers are to be served with at most 20 notes per withdrawal.
> The ATM machine has stock of fifty
> 500 rupee notes and a sufficient number of notes of other denominations.
(i) If the ATM machine dispenses one
(ii) 500 rupee note, for the total number of notes less than or equal to 20, notes of 200 rupee denominations has to be maximum.
500 × 1 + 200 × 22 + 100 × 1 = 5000
i.e., the minimum number of notes = 24
(iii) If the ATM machine dispenses two 500 rupee notes, for the total number of notes less than or equal to 20, notes of 200 rupee denominations has to be maximum.
500 × 2 + 200 × 20 = 5000 i.e., the minimum number of notes = 22
(iv) If the ATM machine dispenses three 500 rupee notes, for the total number of notes less than or equal to 20, notes of 200 rupee denominations has to be maximum.
500 × 3 + 200 × 17 + 100 × 1 = 5000
i.e., the minimum number of notes = 21
(v) If the ATM machine dispenses four 500 rupee notes, for the total minimum number of notes, notes of 200 rupee denominations has to be maximum.
500 × 4 + 200 × 15 = 5000
i.e., the minimum number of notes = 19
Therefore, if the ATM dispenses 4 notes of 500 rupees then it can serve a maximum of 12 customers with 50 notes.
Hence, option (b).