If the day before yesterday was Saturday,what day will fall on the day after tomorrow?

$A$ monkey climbs $30$ feet at the beginning of each hour and rests for a while,during which he slips back $20$ feet before he again starts climbing at the beginning of the next hour. If he begins his ascent at $8:00 \, a.m.$,at what time will he first touch a flag at $120$ feet from the ground?

$(I)$ Kamal is available at home from $12$ noon to $4 \,p.m.$ on Tuesday,Thursday,and Sunday.
$(II)$ His younger brother Navin is available at home on Monday,Thursday,Friday,and Sunday between $10 \,a.m.$ to $2 \,p.m.$
$(III)$ The eldest brother Rajiv is available between $9 \,a.m.$ to $12$ noon on Monday,Wednesday,and Thursday and $2 \,p.m.$ to $4 \,p.m.$ on Friday,Saturday,and Sunday.
On which day$(s)$ of a week,the youngest and the eldest brothers are available at home at the same time?

In a class of $40$ students,Samir's rank from the top is $12^{th}$. Alok is $8$ ranks below Samir. What is Alok's rank from the bottom?

In a queue,Amrita is $10^{th}$ from the front while Mukul is $25^{th}$ from behind and Mamta is just in the middle of the two. If there are $50$ persons in the queue,what position does Mamta occupy from the front (in $^{th}$)?

Count each $1$ in the following sequence of numbers that is immediately followed by $2$,if $2$ is not immediately followed by $3$. How many such $1$'s are there?
$1, 2, 1, 3, 4, 5, 1, 2, 3, 5, 2, 1, 2, 6, 1, 4, 5, 1, 1, 2, 4, 1, 2, 3, 2, 1, 7, 5, 2, 1, 2, 5$