The issue that the Virginia and New Jersey plans were attempting to resolve was the issue of the number of Each state's representatives in Congress.
The Virginia Plan was a proposal by the representatives of Virginia for Bicameral Legislative Branch. This plan is significant for its performance in establishing the stage for the convention and, in particular, for the formulation of the idea of representation as according to the population. Whereas the Virginia Plan was an acknowledgement to the New Jersey Plan of June 1787, hence this Virginia plan called for Bicameral in Congress.
Although some ideas were taken from The New Jersey plan, initially it was refused as a basis for the new constitution. Hence the Virginia plan was adopted in the formation of the new constitution. And the most extensive use of these plans was used by the Connecticut Compromise ( which in part set the legislative structure and representation that each state would have), that placed a Bicameral authority by the House of Representatives of the United States, elected by the American people, and that the Senate provided equality of votes to each state as the New Jersey Plan requested.