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

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

John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone?

Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is

Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is

A water tank has inlets of two types $A$ and $B$. All inlets of type $A$ when open, bring in water at the same rate. All inlets of type $B$, when open, bring in water at the same rate. The empty tank is completely filled in $30$ minutes if $10$ inlets of type $A$ and $45$ inlets of type $B$ are open, and in $1$ hour if $8$ inlets of type $A$ and $18$ inlets of type $B$ are open. In how many minutes will the empty tank get completely filled if $7$ inlets of type $A$ and $27$ inlets of type $B$ are open?

Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been