THE MONEY

Number Theory Level 2

Firoz has a certain amount of money in only Re 1 and Rs 10 notes. The number of Re 1 notes multiplied by the number of Rs 10 notes is equal to the total money (in Rs) that he has. The number of Rs 10 notes is less than ten. Which of the following is a possible figure for the total number of notes he can have?

20 18 14 16

Shreyas Shastry by shreyas shastry , 22, India

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2 solutions

M Saad Rehman
Mar 28, 2014

maximum will be 22 and minimum will be 18 its simple

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Shreyas Shastry
Mar 27, 2014

Let Firoz have n Rs10 notes and m Re 1 notes.

Given 10n+m=nm

=> m=10n/ (n−1)

Since, n<10 the possible values of n for which m is an integer are 2,3 and 6

Corresponding m=20,15 and 12

n+m is either 22 or 18

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