Numerical Appli...

$$A, B$$ and $$C$$ complete a piece of work in $$25, 20$$ and $$24$$ days respectively. All work together for $$2$$ days and then $$A$$ and $$B$$ leave the work . $$C$$ works for next $$\displaystyle8\frac{3}{5}$$ days and then $$A$$ along with $$D$$ join $$C$$ and they all finish the work in next three days. In how many days $$D$$ alone can complete the whole work ?

Two pipes can fill a tank in $$25$$ and $$30$$ minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in $$15$$ minutes. The capacity of the tank is:

A can complete a piece of work in $$18$$  days, B in $$20$$  days and C in $$30$$  days. B and C together start the work and forced to leave after  $$ 2 $$ days. the time taken by A alone to complete the remaining work is 

$$A$$ can do a work in $$15$$ days and $$B$$ can do the same work in $$ 20$$ days, if $$A$$ and $$B$$ has done work for $$4$$ days together, the fraction of work left?

Two pipes can fill an empty tank separately in  $$24$$  minutes  and  $$40$$ minutes respectively and a third pipe can empty  $$30$$  gallons of water per minute. If all the three pipes are open, empty tanks becomes full in one hour. The capacity of tank (in gallons) is 

A tap A can fill a cistern in $$8$$ hours while tap B can fill it in $$4$$ hours. In how much times will the cistern be filled if both A and B are opened together?

In half of a 600 square meters field, a fanner sowed ragi, in one-third of the remaining, he sowed coconut and in one-fourth of the left over, he sowed groundnut. He left half of the remaining land uncultivated. In one-third of the land still left, he dug a well, utilising the remaining land for growing orchids. What fraction of the total land is he using for orchid cultivation?

If a pipe fills the tank in $$10$$ minutes, how much minutes it will take to half fill the tank in we connect two pipes?

If $$15$$ men complete a task in $$3$$ days, how many days will  $$9$$  men take to complete it?

If $$6$$ painters can complete $$9$$ drawing in $$5$$ hours then, what is relation between no. of painters and no. of drawings if no. of hours is constant?