Question

An engine does 10 J of work and exhausts 25 J of waste heat during each cycle.

Answer 1

The thermal efficiency is defined as follows

$\eta = 1 - \frac{Q_{\text{out}}}{Q_\text{in}}$,

and the energy which is put into the system is

$Q_{\text{in}} = W_\text{out} + Q_\text{out}$.

In your case $Q_\text{in} = 25 \text{ J},W_\text{out}=10 \text{ J}.$

So $Q_\text{out}=10 \text{ J}$ which gives an efficiency of

$\eta = 1 - \frac{10 \text{ J}}{25 \text { J}} = 0.6 = 60 \%$.