CAT (QA) PYQs

When they work alone, $B$ needs $25 \%$ more time to finish a job than $A$ does. They two finish the job in $13$ days in the following manner: $A$ works alone till half the job is done, then $A$ and $B$ work together for four days, and finally $B$ works alone to complete the remaining $5\%$ of the job. In how many days can $B$ alone finish the entire job?

A group of $N$ people worked on a project. They finished $35 \%$ of the project by working $7$ hours a day for $10$ days. Thereafter, $10$ people left the group and the remaining people finished the rest of the project in $14$ days by working $10$ hours a day. Then the value of $N$ is

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?