stuff+for+raining+days

Just in case it rains, here are some puzzles for rainy days.

Puzzle One I am an eleven letter word. The first, second, third and fourth letter combine to form a bank’s name. The fifth, sixth and seventh letter combine to form a way of living. The eighth, ninth, tenth and eleventh letter combine to form a mode of transport. What word am I?

Puzzle Two Adam gave one half of the apples he had plus one of Eve. He gave half of the remaining ones plus one more to Diana. Now Adam was left with one apple. How many did he have at the beginning?

Puzzle Three

While boarding a bus you notice that there are 7 girls in the bus already. All the girls have 7 bags each. In each bag there are 7 adult cats. Each of the adult cat have 7 little one. Each of the cat has 4 legs.

Can you calculate the number of legs in the bus ?

Puzzle Four

A couple went on for a climbing trip. But only the husband returned from the vacation and said that his wife slipped off while climbing and died. On investigating, the local sheriff arrested him saying, 'Your travel agent called. You murdered your wife.'

The man did not inform anyone about the trip. Then how did the agent know that it is a murder?

Puzzle Five

Can you transform the word THINK into BRAIN while changing only one letter at a time in a manner that each of the word in the process is a real word ?