What is more useful when it is broken?

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

There are three boxes on a table. One of the box contains Gold and the other two are empty. A printed message contains in each box. One of the message is true and the other two are lies.

The first box says "The Gold is not here".

The Second box says "The Gold is not here".

The Third box says "The Gold is in the Second box".

Which box has the Gold?

What brings you down but never up?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?

John asked Jack, "The time right now is 7 pm. Can you tell me what will be the time 23, 999, 995 hours later ?"

While Bella does not know the answer, do you ?

Can you find a rabbit in the given picture?

Replace the question mark with the correct number in the below-given picture?

A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?