This is an announcement for the paper "Modified Busemann-Petty problem on sections of convex bodies" by A.Koldobsky, V.Yaskin and M.Yaskina. Abstract: The Busemann-Petty problem asks whether origin-symmetric convex bodies in $\mathbb{R}^n$ with smaller central hyperplane sections necessarily have smaller $n$-dimensional volume. It is known that the answer is affirmative if $n\le 4$ and negative if $n\ge 5$. In this article we modify the assumptions of the original Busemann-Petty problem to guarantee the affirmative answer in all dimensions. Archive classification: Functional Analysis Mathematics Subject Classification: 52Axx Remarks: 17 pages The source file(s), modBP.tex: 33931 bytes, is(are) stored in gzipped form as 0410496.gz with size 10kb. The corresponding postcript file has gzipped size 64kb. Submitted from: yaskinv@math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0410496 or http://arXiv.org/abs/math.FA/0410496 or by email in unzipped form by transmitting an empty message with subject line uget 0410496 or in gzipped form by using subject line get 0410496 to: math@arXiv.org.