CAT (QA) PYQs

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?

Two pipes $A$ and $B$ are attached to an empty water tank. Pipe $A$ fills the tank while pipe $B$ drains it. If pipe $A$ is opened at $2$ pm and pipe $B$ is opened at $3$ pm , then the tank becomes full at $10 \mathrm{pm}$. Instead, if pipe $A$ is opened at $2 \mathrm{pm}$ and pipe $B$ is opened at $4 \mathrm{pm}$, then the tank becomes full at $6 \mathrm{pm}$. If pipe $B$ is not opened at all, then the time, in minutes, taken to fill the tank is

Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?