Among the given numbers, the smallest number which when divided by $9$, $10$, $15$ and $20$ leaves remainders $4$, $5$, $10$ and $15$ respectively is

Explanation

Let the required number be $N$ $N \equiv 4 \pmod{9}$ $N \equiv 5 \pmod{10}$ $N \equiv 10 \pmod{15}$ $N \equiv 15 \pmod{20}$ So $9 - 4 = 10 - 5 = 15 - 10 = 20 - 15 = 5$ $N = LCM(9,10,15,20) - 5$ $LCM = 180$ $N = 180 - 5 = 175$ Next possible value $N = 360 - 5 = 355$