Competition among Nihar, PiHan and Calvin!

Nihar received $2N$ dollars and PiHan received $2N +1$ , $2N +2$ , $2N +3$ , $2N + 4$ or $2N + 5$ dollars depending on what residue class $N$ belongs to modulo $5$ . But since PiHan gets $\$5$ bills, his amount is divisible by $5$ . Calvin will then receive either $\$5$ more than PiHan (if PiHan's amount is not divisible by $10$ ) or $\$10$ more than PiHan (if PiHan's amount is divisible by $10$ ). Clearly $2N +5$ is odd, thus not divisible by $10$ . So the maximum occurs when PiHan receives $2N + 4$ dollars, which means 2N \equiv 1 \text{ mod } 5 , i.e. N \equiv 3 \text{ mod } 5 , and that maximum (what Calvin receives) is $2N + 14$ .

Here N should be valid for any integer for given conditions...Let's decide N for N<=10..Let M and R are number of dollar bills for 5 dollar and 10 dollar respectively..

Here 2N<5M so 2N+Y=5M..Now here Y should be maximum..So to maximize Y N=3..as 5M is just greater than 2N..M=2..Y=4..Now 10R just greater than 5M is 20 dollars..So 5M+10=10R..So max 10R in terms of N is 2N+4+10=2N+14..