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Three server A,B & C. How to ssh connect from A to C via intermediate server B, if A to B & C to B are password less(key)? I encountered this in an interview. Anyone knows how?

You are in server A:

ssh user@serverB ssh user@serverC 

Or you can use proxy command (see here for more info Proxies and Jump Hosts) as follows:

Create a config file under ~/.ssh in server A with following data:

Host serverC
 HostName serverC
 User user
 ProxyCommand ssh -l user serverB -W %h:%p

Then you can just user ssh serverC to reach it from serverA via serverB.

@coffeMug I tried out your 1st solution, it will work only if B->C
also is password less isn't ? here in my case A->B & C->B are password
less. but not B-> C.

Maybe, and only maybe C have a config allowing A, but does not communicate directly to A, requiring the middle server B only for the network communication. If that is true. iptables on server B using the table nat can do something for you.

Sorry i tried to help... so give it a try, is the only possibility, because in all others it will ask you for a password, because B->C no-password is required to this get working using ssh only.

The original question does not make much sense. But I can guess they wanted to ask about the servers A and C in private networks (so they do not "see" each other) and B visible to both of them. In this case, the answer is Remote Port Forwarding. With example:

Create a tunnel B->C from C:

C$ ssh -R 2222:localhost:22 B

and then connecting from A to C like this:

A$ ssh A ssh -p 2222 localhost

Or in more elegant way with ssh_config. You will have to certainly write the password to connect to the server C (localhost:2222 from B), if there is not set up pubkey authentication, but that should not be a problem.