Reaching the place of meeting on Tuesday $15 \,minutes$ before $08:30 \,hours$,Anuj found himself half an hour earlier than the man who was $40 \,minutes$ late. What was the scheduled time of the meeting?

Rahul ranked ninth from the top and thirty-eighth from the bottom in a class. How many students are there in the class?

There are $35$ students in a class. Suman ranks $3^{rd}$ among the girls in the class. Amit ranks $5^{th}$ among the boys in the class. Suman is one rank below Amit in the class. No two students hold the same rank in the class. What is Amit's rank in the class?

Three persons $A, B$ and $C$ are standing in a queue. There are $5$ persons between $A$ and $B$ and $8$ persons between $B$ and $C$. If there are $3$ persons ahead of $C$ and $21$ persons behind $A$, what could be the minimum number of persons in the queue?

In a row of $21$ girls, when Monika was shifted by four places towards the right, she became $12^{th}$ from the left end. What was her earlier position from the right end of the row (in $^{th}$)?

The train for Lucknow leaves every two and a half hours from New Delhi Railway Station. An announcement was made at the station that the train for Lucknow had left $40 \,minutes$ ago and the next train will leave at $18:00 \,hrs.$ At what time was the announcement made?