Since only one meter is allowed, a non-ideal voltmeter should be used. However, an ammeter could also do the trick.
Work Step by Step
The non-ideal voltmeter has finite resistance, and some current will flow. We are told that this is a real battery with nonnegligible internal resistance, so this current will lower the terminal voltage (page 833) by a larger amount as the battery ages and the internal resistance increases. The voltmeter can read this terminal voltage. If one had an ammeter that could read very large currents, that could also be used. One would short-circuit the battery (which is generally not a good idea), allowing a large current to flow. Over time, as the battery’s internal resistance increased, the current would decrease.