What is the Surname of Barbie Doll?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

A pond had 60 fish, out of which, all but 20 died.
How many fishes are now present in that pond?

A man is surviving on an island along with his friend. They have been starving for four days for food. Suddenly, they find a fisherman. The friend goes with the fisherman in order to catch the fish (if they can find any).

The fisherman returns after some time but he is alone and has some salmon that he had prepared. When asked, the fisherman tells him that his best friend fell off the boat and drowned in the water. Starving for so long, he eats the meal while crying for his friend.

After being rescued, he goes to a diner and orders salmon. When he eats his meal, he jumps and commits suicide. Why did he do it?

At my favorite fruit stand,
an orange costs 18,
a pineapple costs 27,
and a grape costs 15.
Using the same logic, can you tell how much a mango costs?

In a stable, there are men and horses. In all, there are 22 heads and 72 feet. How many men and how many horses are in the stable

You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

Evil warlock dislikes dwarfs and therefore he selects four of them and buries them. The dwarfs are buried in the ground and they are in such a way that except for their heads, their body is inside the ground. The dwarfs cannot move their body and they can view only forward. They are all buried in a line, and amongst the four, one of the dwarfs is separated by a wall. All the dwarfs are in the same direction. The last dwarfs can see two heads of friends in the front and a wall. In the last second dwarf can see one head of his friend and a wall. The second dwarf can see only the wall. The dwarf can see nothing.
Warlock comprehends the situation and tells the dwarfs that he has placed hats on their heads. There are two blue hats and two red ones. In all four dwarfs, one of them has to say what colour hat he is wearing. If the dwarf says the correct colour of the hat, they will be left free. If the answer is wrong, then they will be dug inside the ground till the very end.

What will be the answer by the dwarf and how will they answer?

A solo dice game is played. In this game, upon each turn, a normal pair of dice is rolled and the score is calculated not by adding the numbers but multiplying them.

In a particular game, the score for the second roll is five more than what was achieved in the first roll. The score for the third roll is six less than what was completed in the second roll. The score for the fourth roll is eleven more than what was achieved in the third. The score for the fifth roll is eight less than what was completed in the fourth.

Can you calculate the score for each of the five throws?

I know a nine-letter word having only one vowel.
Do you ?