Step 1: Compute individual costs.
Take the weights as $12,15,20$ kg.
Cost$_1=12\times 100=₹ 1200$, Cost$_2=15\times 80=₹ 1200$, Cost$_3=20\times 60=₹ 1200$.
\Rightarrow\ Total cost $=₹ 3600$ (each kind costs ₹ 1200).
Step 2: Selling price of first two.
Cost of first two $=₹ (1200+1200)=₹ 2400$.
Given profit $=20\%$ on these, so SP$_{12}=1.2\times 2400=₹ 2880$.
Step 3: Use overall no-profit-no-loss.
Overall SP $=$ Total cost $=₹ 3600$.
\Rightarrow\ SP of third $=₹ 3600-₹ 2880=₹ 720$.
Step 4: Loss\% on third.
Loss $=₹ (1200-720)=₹ 480$.
Loss\% $=\dfrac{480}{1200}\times 100=40\%$.
\Rightarrow\ \boxed{40\%}.