A reversible engine has an efficiency of $\frac{1}{4}.$ If the temperature of the sink is reduced by $58K,$ its efficiency becomes double. Calculate the temperature of the sink:

Efficiency of heat engine 

$\eta =1-\frac{T_s}{T}\Rightarrow \frac{1}{4}=1-\frac{T_s}{T}$ [ $T_s\to$ sink temperature]

$\Rightarrow 4T_s=3Tor,T_s=\frac{3}{4}T \dots \dots \dots \left(i\right)$

$\Rightarrow \frac{1}{2}=1-\frac{T_s-58}{T} \dots \dots \dots \left(ii\right)$

From equation (i) & (ii)

$\frac{3}{4}=\frac{58}{T}+\frac{1}{2}\Rightarrow \frac{1}{4}=\frac{58}{T}\Rightarrow T=232$

$\therefore T_s=\frac{3}{4}T={174}^{0}C$