How can a man go eight days without sleep?

Find the next number in the series.
1 10 24 43 67 ?

A landlord calls both of his sons and tells them that their horses will now decide who will transfer the inheritance. He tells them to race along the land till the end and the one whose horse will be slower will win and be the heir to all the property.

Both of them keep wandering for days but to no result. Then they ask a wise man regarding it. The man advises them on the matter after which they jump on the horses and race as fast as they can till the end. Why did they do it?

What did the wise man say?

There is a box. The area of its top is 240 square units, the area of the front is 300 square units and the area of the end is 180 square units.

Can you calculate the dimensions of this box with the given data?

In one of the popular batman series movie "Batman Forever", there was a riddle that goes like "Tear me off and then scratch my head and I was red then and now I am back. Who am I?

Can you move 2 matchsticks to form four equal sized squares.

There’s a girl who has a large family. She has an equal amount of brothers and sisters, but each brother only has half as many brothers and sisters. What’s the correct amount of brothers and sisters?

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

The following four words might seem abrupt to you. But you can make them meaningful by just adding vowels.
RDSH
GGPLNT
TMT
NN

Hint: All of them are vegetables.

Replace the question mark with the number below given a simple math problem.