A reversible engine has an efficiency of $\frac{1}{4}$. If the temperature of the sink is reduced by $58^{\circ} {C}$, its efficiency becomes double. Calculate the temperature of the sink. (In $^{\circ} {C}$)
JEE MAIN 2021, Diffcult
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${T}_{2}=$ sink temperature
$\eta=1-\frac{{T}_{2}}{{T}_{1}}$
$\frac{1}{4}=1-\frac{{T}_{2}}{{T}_{1}}$
$\frac{{T}_{2}}{{T}_{1}}=\frac{3}{4} \ldots$ $(i)$
$\frac{1}{2}=1-\frac{{T}_{2}-58}{{T}_{1}}$
$\frac{{T}_{2}}{{T}_{1}}-\frac{58}{{T}_{1}}=\frac{1}{2}$
$\frac{3}{4}=\frac{58}{{T}_{1}}+\frac{1}{2}$
$\frac{1}{4}=\frac{58}{{T}_{1}} \Rightarrow {T}_{1}=232$
${T}_{2}=\frac{3}{4} \times 232$
${T}_{2}=174\, {K}$
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