The interrelationship between affine resolvability and variance balancedness and the relation \(b=v+t-1\) has been explored. It is proved that an incomplete block affine resolvable design with \(b=v+t-1\) is not necessarily variance-balanced. A necessary and sufficient condition for an affine-resolvable design satisfying \(b=v+t-1\) to be variance-balanced has been derived. Interestingly, the authors have set an open problem with regard to the existence of an incomplete block 1-resolvable variance-balanced design with \(b=v+t-1\), having unequal block sizes in a set.