**Solution:**Let cost of A be Rs $x$ and of B be Rs $y$.

Given, Total cost $=Rs2775$

$=>x+y=2775$ --- (1)

Also, cost of an article A is $15$ % less than that of article B

=> $x=y−0.15y=>x=0.85y$ --- (2)

From $(1)$ and $(2)$, we get

$0.85y+y=2775$

$1.85y=2775$

$=>y=1500$

And, $x=0.85y=1275$

Hence, cost of A is Rs $1275$ and of B is Rs $1500$