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A worker joins or replaces another midway: newcomer's time for a part of the work

This type of question, asked 2 times: 3 Feb 2022 Tier II, 18 Jan 2026 Tier II. All 2 questions below, oldest first.

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  1. Question 1

    3 Feb 2022 Tier II

    2
    P can finish a work in 18 days. When he had worked for 5 days, Q joined him. If both of them together completed the remaining work in 135\frac{13}{5} days, then in how many days can Q alone finish 6623%66\frac{2}{3}\% of the same work?

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  2. Question 2

    18 Jan 2026 Tier II

    19
    P and Q can do a piece of work in 20 days and 30 days, respectively. They work together for 6 days, and then Q is replaced by R. If the rest of the work is completed by P and R in 8 more days, in how many days can R alone complete 60% of the work?

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