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GATE Mechanical 2016 Set 1 | GA Question: 10

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$P$, $Q$, $R$ and $S$ are working on a project. $Q$ can finish the task in $25$ days, working alone for $12$ hours a day. $R$ can finish the task in $50$ days, working alone for $12$ hours per day. $Q$ worked $12$ hours a day but took sick leave in the beginning for two days. $R$ worked $18$ hours a day on all days. What is the ratio of work done by $Q$ and $R$ after $7$ days from the start of the project?

  1. $10:11$
  2. $11:10$
  3. $20:21$
  4. $21:20$
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GATE Mechanical 2016 Set 1 | GA Question: 9
If $q^{-a}=\displaystyle{\frac{1}{r}}$ and $r^{-b}=\displaystyle{\frac{1}{s}}$ and $s^{-c}=\displaystyle{\frac{1}{q}}$, the value of $abc$ is $(rqs)^{-1}$ $0$ $1$ $r+q+s$
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