A and C together can complete a certain work in 30 days. B is 20% more efficient than C. A, B and C together can do the same work in 20 days. C alone completed one fourth of the work and the remaining work was completed by A and B together. In how many days was the entire work completed?

81 equally efficient people could complete a piece of work in 15 days. Initially 45 such people started working together. But after they worked together for 6 days their employer wanted that the work should be completed in a total of 21 days. However any new worker who joins is only $60\%$ as efficient as any of the 45 people already working. How many new workers did the employer hire to work alongside the initial 45 people to meet the deadline?

Sahil can complete a job in 20 days when working alone. Manoj is twice as fast as Sahil and three times as fast as Ashish in the same job. The collaborative work arrangement involves Sahil and Manoj working on the first day, Sahil and Ashish on the second day, and Manoj and Ashish on the third day. This three-day cycle continues till the work is complete.

What fraction of the total work will then be done by Ashish till the job is completed?

A, B and C work in a workshop for creating identical idols. A can craft 10 idols in 150 days. Similarly, B and C can individually create 16 idols in 192 days and 320 days, respectively. B works every day, A works only on alternate days starting from the first day, i.e. 1st March, and C also works only on alternate days starting from the second day, i.e 2nd March. On which date will the construction of 2 idols be completed?

Two inlet pipes A and B can fill a tank in 18 hours and 24 hours, respectively, while an outlet pipe C can empty the full tank in X hours. Initially, all three pipes are opened together. After 8 hours, pipe B is closed, and another 6 hours later, pipe C is also closed. The remaining portion of the tank is then filled by pipe A alone. If the tank gets completely filled in a total of 16 hours, find the value of X.