Originally Posted by Jjanel

Look at: lvresize -r (--resizefs) in man page

Basically, this is often done; if done right, no loss; if done wrong, disaster!
Shrinking the device without first shrinking the filesystem will destroy the filesystem.
"thank you so much"
it is indeed very informative . but the thing is, i am actually finding something for my own logic. i mean i know for shrinking or for reducing a logical volume you first have to unmount it and then the resizing thing .but what i have asked for is that what will happen with the data i mean on which side it will go .i mean i need the concept and definitely the explanation for it ..
thank you again

Here's a LQ Thread that might be relevant, found from a web-search of:
lvreduce|lvresize tutorial move data

Welcome to LQ! Let us know what you will try or further questions after reading for a while.

p.s. post relevant info, like: pvs;vgs;lvs;lsblk -fp ...etc

Originally Posted by sundialsvcs

When you resize the volume, one option that's available will (first) resize the file system, thus protecting your data. (Any data that is located in areas of the volume that are about to disappear will be moved out of harm's way.)

In my opinion, you always want to use LVM, and you'll see why the moment that your hard drive fills up.

Without LVM, that's a very messy situation to get out of. With LVM it is easy: just add another physical volume, map it to the appropriate logical pool, and resize the filesystem upward. Done. (And you don't even have to reboot the system.)

LVM separates the logical notion of a "mount point" from the physical resource(s) that correspond to it, allowing the data to be distributed among many physical volumes in various useful ways.

Don't be "doubtful" about this important feature. Use it!