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?

Anil alone can do a job in $20$ days while Sunil alone can do it in $40$ days. Anil starts the job, and after $3$ days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done $10\%$ of the job, then in how many days was the job done?

A person can complete a job in $120$ days. He works alone on Day $1$. On Day $2$, he is joined by another person who also can complete the job in exactly $120$ days. On Day $3$, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?