An engine has an efficiency of 1/6. When the temperature of the sink is reduced by 62℃, its efficiency is doubled. What is the temperature of the source?

The efficiency of a heat engine is given by: η = 1 - T₂/T₁.

From the given data, we have:
η₁ = 1 - T₂/T₁ = 1/6 => T₂/T₁ = 5/6
η₂ = 2η₁ = 1/3 => T₂₂/T₁ = 2/3

T₂₂ = T₂ - 62

Substituting T₂₂ in the second equation:
(T₂ - 62)/T₁ = 2/3

Since T₂/T₁ = 5/6, we can write T₂ = (5/6)T₁

Substituting this into the equation above:
((5/6)T₁ - 62)/T₁ = 2/3
(5/6)T₁ - 62 = (2/3)T₁
(5/6)T₁ - (2/3)T₁ = 62
(1/6)T₁ = 62
T₁ = 372 K = 99℃