What is the problem behind this if we connect charger to a laptop its not charging in one of laptop if we connect it to another laptop its charging?

If there is issue related to battery then your laptop either give "plugged in but not charging" message at power option menu or would not detect battery at all and give message "plugged in or no battery".

Mostly the first case is related to incompatibility issue related to the current and voltage difference between battery requirement and charger supplying.

The later case prove to be an issue with battery cells.

It could be a variations of things from the charging port, battery, components inoperable,compatibility issues, etc. 

Troubleshooting helps tremendously.

might be compatibility problem and, if type of laptop is same then its battery problem.

If 2 laptops charging port is same then one laptop have must battery problems. 

FIRST OF ALL POWER ON THE LAPTOP WITHOUT BATTERY USING THE POWER ADAPTOR IF IT STARTS THEN IT  WAS THE BATTERY RELATED ISSUE. CHANGE THE BATTERY OF THE LAPTOP. IF STILL THE PROBLEM PERSISTS THEN CHECK THE POWER ADAPTOR JACK.

It's either the charger is not compatible with the model of the laptop or the charging port is faulty. 

Faulty battery may be another issue...

It might be problem in charging port or the charging module connection from motherboard in laptop is malfunctioning.

Another possibility of not charging: Battery internal circuit regulator is faulty.

Possible reasons:

1. The battery not connected correctly. Try reconnecting it. (if possible)
2. The battery contacts are dirty or oxidized and it’s not making good connection with the motherboard. Apply some electronic contact cleaner on the contacts then reconnect the battery (if possible).
3. If reconnecting the battery doesn’t help, most likely the battery is bad and will need to be replaced.
4. If you replaced the battery but the problem still exists, this is a motherboard failure. Likely the charging circuit on the motherboard has failed (usually a blown diode). In this case the whole motherboard has to be replaced (or repaired).

Cheers.

Battery is end of life. Need to change battery from first laptop

Sir,

 The connector of the first laptop is damage so replace it with new one and then connect the charger ,now it will charging,,,,,,,,,,,,

 i think there is lose on the Laptop power connector or IC charger need to replace