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SET 1 — 🔍 CAT Level
At the beginning of a day, Rajat had a total of ₹1300 with him, in notes of exactly three denominations – ₹10, ₹50 and ₹100. During the day, he made exactly eight transactions at different times, in each case using only the notes present in his wallet at the time of making the transaction. In each transaction, the notes that he received, if any, were also of the three denominations mentioned above. Further, in each transaction, Rajat always gave the notes first before receiving any notes in return.
The following table provides the time at which each of the eight transactions took place, the number of notes of each denomination that he gave and the number of notes of each denomination that he received.
Time | Notes Given ₹10 | ₹50 | ₹100 | Notes Received ₹10 | ₹50 | ₹100 |
|---|---|---|---|---|---|---|
10:00 AM | 0 | 0 | 2 | 3 | 1 | 0 |
10:35 AM | 7 | 2 | 0 | 2 | 0 | 0 |
11:35 AM | 0 | 2 | 3 | 1 | 0 | 0 |
12:25 PM | 0 | 2 | 3 | 4 | 0 | 1 |
1:45 PM | 6 | 0 | 0 | 1 | 0 | 1 |
3:15 PM | 4 | 0 | 0 | 1 | 2 | 2 |
4:50 PM | 8 | 1 | 5 | 2 | 3 | 2 |
5:30 PM | 0 | 1 | 0 | 0 | 0 | 2 |
Question 1
What is the total number of notes that he had in his wallet at the beginning of the day?
Question 2
What is the total number of notes in his wallet at the end of the day?
Question 3
What is the highest number of ₹10 notes in his wallet at any point of time during the day?
A. 21
B. 18
C. 15
D. 11
Question 4
At which of the following times would he have at least six ₹100 notes in his wallet?
A. 11:00 AM
B. 3:30 PM
C. 12:00 PM
D. More than one of the above
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✅ Answers & Explanations
Let a be the number of ₹10 notes, b be the number of ₹50 notes and c be the number of ₹100 notes in his wallet at the beginning of the day.
The following table gives the notes in his wallet after each transaction:
Time | Notes in Wallet after Giving | Notes in Wallet after Receiving | ||||
|---|---|---|---|---|---|---|
₹10 | ₹50 | ₹100 | ₹10 | ₹50 | ₹100 | |
10:00 AM | a | b | c − 2 | a + 3 | b + 1 | c − 2 |
10:35 AM | a − 4 | b − 1 | c − 2 | a − 2 | b − 1 | c − 2 |
11:35 AM | a − 2 | b − 3 | c − 5 | a − 1 | b − 3 | c − 5 |
12:25 PM | a − 1 | b − 5 | c − 8 | a + 3 | b − 5 | c − 7 |
1:45 PM | a − 3 | b − 5 | c − 7 | a − 2 | b − 5 | c − 6 |
3:15 PM | a − 6 | b − 5 | c − 6 | a − 5 | b − 3 | c − 4 |
4:50 PM | a − 13 | b − 4 | c − 9 | a − 11 | b − 1 | c − 7 |
5:30 PM | a − 11 | b − 2 | c − 7 | a − 11 | b − 2 | c − 5 |
Now, since the number of notes in his wallet at any point cannot be negative,
a must be at least 13
b must be at least 5
c must be at least 9
If:
a = 13
b = 5
c = 9
then the amount in his wallet will be:
130+250+900=1280130 + 250 + 900 = 1280130+250+900=1280
Since he has ₹1300 at the beginning of the day, he must have:
15 ₹10 notes
5 ₹50 notes
9 ₹100 notes
Question 1
What is the total number of notes that he had in his wallet at the beginning of the day?
15+5+9=2915+5+9=2915+5+9=29
Answer: 29 notes
Question 2
What is the total number of notes in his wallet at the end of the day?
From the final row of the table, after the 5:30 PM transaction, the numbers of notes are:
a−11,b−2,c−5
Substituting a=15, b=5, c=9
₹10 notes:
15−11=4
₹50 notes:
5−2=3
₹100 notes:
9−5=49
Hence, the total number of notes at the end of the day is:
4+3+4=11
Answer: 11 notes
Question 3
What is the highest number of ₹10 notes in his wallet at any point during the day?
Using a=15a=15a=15, the number of ₹10 notes after receiving notes in each transaction was:
Time | Number of ₹10 notes |
|---|---|
Beginning | 15 |
10:00 AM | (a+3=18) |
10:35 AM | (a-2=13) |
11:35 AM | (a-1=14) |
12:25 PM | (a+3=18) |
1:45 PM | (a-2=13) |
3:15 PM | (a-5=10) |
4:50 PM | (a-11=4) |
5:30 PM | (a-11=4) |
The maximum number is:
18
Answer: Option B — 18
Question 4
At which of the following times would he have at least six ₹100 notes in his wallet?
The number of ₹100 notes at different stages is obtained using c=9.
At 11:00 AM
11:00 AM falls between the 10:35 AM and 11:35 AM transactions.
After the 10:35 AM transaction, he had:
c−2=9−2=7
₹100 notes.
Thus, he had at least six ₹100 notes.
At 12:00 PM
12:00 PM falls between the 11:35 AM and 12:25 PM transactions.
After the 11:35 AM transaction, he had:
c−5=9−5=4
₹100 notes.
Thus, he did not have at least six notes.
At 3:30 PM
3:30 PM falls between the 3:15 PM and 4:50 PM transactions.
After the 3:15 PM transaction, he had:
c−4=9−4=5
₹100 notes.
Thus, he did not have at least six notes.
Therefore, only 11:00 AM satisfies the condition.
Answer: Option A — 11:00 AM
Final answers
29 notes
11 notes
18 — Option B
11:00 AM — Option A
⚡ Brain teasers are not just about getting the right answer — they train you to think differently under pressure.
Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.
See you in tomorrow’s challenge!