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Carnot engine efficiency doubles when the sink temperature is lowered by a few degrees: find the source or sink temperature

The same question, asked 2 times: 2021 Paper 15*, 2021 Paper 22. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 15

    15
    The efficiency of heat engine is 16\frac{1}{6}. When the temperature of sink is reduced by 62∘C62^{\circ}C, then efficiency doubles. What is the temperature of the source?

  2. Question 2

    2021 Paper 22

    4
    A reversible engine has an efficiency of 14\frac{1}{4}. If the temperature of the sink is reduced by 58∘C58^{\circ}C, its efficiency becomes double. Calculate the temperature of the sink:

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