Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:

$$\eqalign{ & {\text{Original}}\,{\text{share}}\,{\text{of}}\,{\text{1}}\,{\text{person}} = \frac{1}{8} \cr & {\text{New}}\,{\text{share}}\,{\text{of}}\,{\text{1}}\,{\text{person}} = \frac{1}{7} \cr & {\text{Increase}} = {\frac{1}{7} \times \frac{1}{8}} = \frac{1}{{56}} \cr & \therefore {\text{Required}}\,{\text{fraction}} \cr & = \frac{{ {1/56} }}{{ {1/8} }} = {\frac{1}{{56}} \times \frac{8}{1}} = \frac{1}{7} \cr} $$