What are you using as a light source? Does ambient light hit the area that the LDR "sees"? If you have fluorescent lights they actually flicker and so you'll see lots of noise. You DMM may show a constant voltage because the DC mode measures just that DC. Try measuring the output in AC mode. It should say 0v or close to it.
So u can't say light is varying.
Hmmm... doesn't sound like it should... but maybe florescent room lights are adding something? Try using our setup with the room lights off, just in case the previous post was on to something?
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Second idea...
Maybe the light from your LEDs is acting in two ways... sometimes doing what you think, and sometimes "reflecting" off of the surface of the surface? Position the LEDs so that any "mirror-like" reflection from them will miss the LRRs... Did I manage to get my idea across?
Can you include the schematics?
It worked when i read on digital pins rather than analog
Can someone describe the problem here?