help me with this before 7:30 in the morning. Tomorrow is my exam.
Is that 4.65 per day? Because if it is, then you are looking for the smallest number $k$ such that $4.65k$ is an integer. Let's rewrite it as a fraction, reduce it, and then the denominator will be the smallest such number:
$4.65 = \dfrac{465}{100} = \dfrac{3\cdot \cancel{5} \cdot 31}{2\cdot 2 \cdot \cancel{5} \cdot 5} = \dfrac{93}{20}$
Since $93 = 31\cdot 3$ and $20 = 2^2\cdot 5$ have no common factors, this fraction is irreducible. Therefore, 20 is the smallest such number.
Is that "4.65" rupees? I don't see why the "least number of days in which he can save an exact number of rupees" is not "1". One one day save 4 rupees, on another day, save 0.65 rupees. The most number of days "in which he can save an exact number of rupees" is 4.
(SlipEternal's interpretation, that he is saving 4.65 rupees per day and the question is when that will add to an integer number of rupees is probably the correct one.)