CAT (QA) PYQs

At their usual efficiency levels, $A$ and $B$ together finish a task in $12$ days. If $A$ had worked half as efficiently as she usually does, and $B$ had worked thrice as efficiently as he usually does, the task would have been completed in $9$ days. How many days would $A$ take to finish the task if she works alone at her usual efficiency?

Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna is the same job. The undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is

Ramesh and Ganesh can together complete a work in $16$ days. After seven days of working together, Ramesh got sick and his efficiency fell by $30 \%$. As a result, they completed the work in $17$ days instead of $16$ days. If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work?