A person X has four notes of Rupee 1, 2, 5 and 10 denomination. The number of different sums of money she can form from them is

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Q: 40 (IAS/2010)
A person X has four notes of Rupee 1, 2, 5 and 10 denomination. The number of different sums of money she can form from them is

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,29,44,21,29,17,6

keywords: 

{'rupee': [1, 0, 1, 0], 'different sums': [0, 0, 2, 0], 'number': [0, 0, 0, 2], 'notes': [0, 0, 1, 1], 'denomination': [0, 0, 1, 0], 'money': [2, 0, 2, 10]}

We can solve this problem by listing out all possible combinations of the given denominations.

Using only one note at a time, we can form the following sums:

1, 2, 5, 10

Using two notes at a time, we can form the following sums:

1+1=2, 1+2=3, 1+5=6, 1+10=11, 2+2=4, 2+5=7, 2+10=12, 5+5=10, 5+10=15

Using three notes at a time, we can form the following sums:

1+1+1=3, 1+1+2=4, 1+1+5=7, 1+1+10=12, 1+2+2=5, 1+2+5=8, 1+2+10=13, 1+5+5=11, 1+5+10=16, 2+2+5=9, 2+2+10=14, 2+5+5=12, 2+5+10=17, 5+5+10=20

Using all four notes, we can form only one sum: 1+2+5+10=18

Therefore, the total number of different sums of money that can be formed using these notes is 15. Answer: 15.