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Finding useful work if you know the efficiency and the work expended can be done by using the concept of energy efficiency. Energy efficiency is the ratio of the output of a system (in this case work) to the input (in this case energy). By knowing the efficiency and the work expended, you can calculate the amount of energy expended in order to produce the given amount of work.

Once you have the energy expended, you can then use this figure to determine the amount of useful work that can be produced. This is done by taking the energy expended and dividing it by the efficiency. The result of this calculation will give you the amount of useful work that can be produced with the given energy expended.

For example, if you have an efficiency of 80% and you know that 10 units of energy were expended to produce a certain amount of work, you can calculate the amount of useful work that can be produced by dividing 10 by 0.8 (which is the same as multiplying by 1.25). The result of this calculation is 12.5 units of useful work.

In summary, finding useful work if you know the efficiency and the work expended can be done by calculating the amount of energy expended and then using the energy efficiency to calculate the amount of useful work that can be produced.