Numerical Appli...

$$12$$ children take $$16$$ days to complete a work which can be completed by $$8$$ adults in $$12$$ days. $$16$$ adults started working and after $$3$$ days, $$10$$ adults left and $$4$$ children joined them. How many days will they take to complete the remaining work ?

Pipe A fills a tank of $$700$$ litres capacity at the rate of $$40$$ litres a minute. Another pipe B fills the same tank at the rate of $$30$$ litres a minute. A pipe at the bottom of the tank drains the tank at the rate of $$20$$ litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow?

Two pipes A and B can fill a tank in $$36$$ hours and $$45$$ hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?

Two pipes A and B can fill a cistern in $$\displaystyle 37\frac{1}{2}$$ min and $$45$$ min respectively. Both pipes were opened and the cistern was filled in just  $$\displaystyle \frac{1}{2}$$ an hour if the pipe B is turned off after what time it is opened? 

A cistern can be filled by a tap in $$4$$ hours while it can be emptied by another tap in $$9$$ hours. If both the taps are opened simultaneously then after how much time will the cistern get filled ?

$$A$$ works twice as fast as $$B.$$ If $$B$$ can complete a work in $$12$$ days independently, the number of days in which $$A$$ and $$B$$ can together finish the work in 

A large tanker can be filled by two pipes $$A$$ and $$B$$ in $$60$$ min and $$40$$ min. respectively. How many minutes will it take to fill the tanker from empty state if $$B$$ is used for half the time and $$A$$ and $$B$$ fill it together for the other half ?

A water tank can be filled by a tap in $$6$$ hours while it can be emptied by another tap in $$8$$ hours. If both the taps are opened simultaneously then after how much time will the tank get filled ?

Two pipes $$A$$ and $$B$$ together can fill a cistern in $$4$$ hours. Had they been opened separately, then $$B$$ would have taken $$6$$ hours more than $$A$$ to fill the cistern. How much time will be taken by $$A$$ to fill the cistern separately ?

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank five hour faster than the first pipe and 4 hour slower than the third. The time required by the first pipe is: