Heat and Thermodynamics

The efficiency formula for a Carnot engine is:
η=1−‌

T2

T1

Here, T1 is the absolute temperature of the source, and T2 is the absolute temperature of the sink.
The problem says the source is 25% hotter than the sink. That means:
T1=T2+0.25×T2=1.25T2
Now, plug T1=1.25T2 into the efficiency formula:
‌η=1−‌

T2

1.25T2

‌η=1−‌

1

1.25

‌‌

1

1.25

=‌

4

5

So,
‌η=1−‌

4

5

‌η=‌

1

5

To change this to a percentage, multiply by 100% :
η=‌

1

5

×100%=20%
So, the engine's efficiency is 20%.