The price of Darjeeling tea ( in rupees per kilogram) is $100 + 0.10 n,$ on $n$-th day of $2007\; (n=1, 2, 3, \dots,100),$ and then remains constant. On the other hand, the price of Ooty tea ( in rupees per kilogram) is $89 +0.15 n$ on the $n$-th day of $2007\; (n=1,2, \dots,365).$ On which date in $2007$ will the prices of these two varieties of tea be equal?
- May $21$
- April $11$
- May $20$
- April $10$
- June $30$