I have website wherein backlinks are increasing but Google SERP is down. Please tell me how it’s possible.

Try to get backlinks with good PR sites.

Are the backlinks valuable, full of good, user-friendly content as well as relevant to your page?

Also consider the age of the links... how old are the pages? the longer a page has been up, the more value it has.

I don't believe that. I think Maybe backlink for your post isn't clear. Maybe, it's not good website . such as sexual website , this not get good backlink sure. Please change to goods web-site and good informative web site is better , One time spend post and get more PR and Backlink.
Try!!!

Where exactly have you been posting at? B/c google loves links, I wish I had it the link but, there is a tool that can evalulate your backlinks and tell you if the search engines see it as spam, matter fact I remember, check out the bad neighborhood tool and run your site thru it, it will pick up links you did not know you even had, and clearly mark next to it "SPAM" and then you need to try to get it removed ASAP.

Same issue is with me.
According to yahoo site explorer my back links are increasing, but rank went down.

Backlink are important for ranking , but good backlinks from authority sites are more important try to get backlinks from PR pages

Don't build too many back links in one day instead start building links slowly.