Two Ideal Carnot Heat Engines Have the Same Efficiency $5.0 \times 10 ^ { 2 } \mathrm {~K}$

Two ideal Carnot heat engines have the same efficiency. One operates between $5.0 \times 10 ^ { 2 } \mathrm {~K}$ and $3.0$ $\times 10 ^ { 2 } \mathrm {~K}$ , and the other between $4.0 \times 10 ^ { 2 } \mathrm {~K}$ and some lower temperature. What is the lower temperature?

A) $280 \mathrm {~K}$
B) $240 \mathrm {~K}$
C) $200 \mathrm {~K}$
D) $220 \mathrm {~K}$
E) $260 \mathrm {~K}$