Numerical Appli...

In how many days can $$10$$ women finish a work?
$$I$$. $$10$$ men can complete the work in $$6$$ days.
$$II$$. $$10$$ men and $$10$$ women together can complete the work in $$3\cfrac{3}{7}$$ days.
$$III$$. If $$10$$ men work for $$3$$ days and thereafter $$10$$ women replace them, the remaining work in completed in $$4$$ days.

$$A$$ and $$B$$ can do a job together in $$7$$ days. $$A$$ is $$1\cfrac{3}{4}$$ times as efficient as $$B$$. The same job can be done by $$A$$ alone in:

How many worker are required for completing the construction work in $$10$$ days?
$$I$$. $$20$$% of the work can be completed by $$8$$ workers in $$8$$ days.
$$II$$. $$20$$ workers can complete the work in $$16$$ days.
$$III$$. One-eighth of the work can be completed by $$8$$ workers in $$5$$ days.

$$8$$ men and $$14$$ women are working together in a field. After working for $$3$$ days, $$5$$ men and $$8$$ women leave the work. How many more days will be required to complete the work?
$$I$$. $$19$$ men and $$12$$ women together can complete the work in $$18$$ days.
$$II$$. $$16$$ men can complete two-third of the work in $$16$$ days.
$$III$$. In $$1$$ day, the work done by three men in equal to the work done by four women.

How long will Machine $$Y$$, working alone, take to produce $$x$$ candles?
$$I$$. Machine $$X$$ produce $$x$$ candles in $$5$$ minutes.
$$II$$. Machine $$X$$ and Machine $$Y$$ working at the same time produce $$x$$ candles in $$2$$ minutes.

$$A$$ and $$B$$ together can complete a task in $$7$$ days. $$B$$ alone can do it in $$20$$ days. What part of the work was carried out by $$A$$?
$$I$$. $$A$$ completed the job alone after $$A$$ and $$B$$ worked together for $$5$$ days.
$$II$$. Part of the work done by $$A$$ could have been done by $$B$$ and $$C$$ together in $$6$$ days.

Two pipes can fill a tank in $$20$$ and $$24$$ 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 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 $$5$$ hours faster than the first pipe and $$4$$ hours slower than the third pipe. The time required by the first pipe is.

Pipes A and B can fill a tank in $$5$$ and $$6$$ hours respectively. Pipe C can empty it in $$12$$ hours. If all the three pipes are opened together, then the tank will be filled in.

A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?