Numerical Appli...

Ram can do a price of work in $$6$$ days and Shyam can finish the same work in $$12$$ days. How much work will be finished if both work together for $$2$$ days?

A can do a piece of work in $$6\dfrac {2}{3}$$ days and B in $$5$$ days. They work together for $$2$$ days and then A leaves B to finish the work alone. How long will B take to finish it?

$$1200$$ men in a fort have provisions for $$28$$ days. After $$4$$ days, $$300$$ men leave the fort. How long will food last now?

In how many ways $$7$$ men and $$7$$ women can be seated around a round table such that no two women can sit together?

A can copy $$75$$ pages in $$25$$ hours, A and B together copy $$135$$ pages in $$27$$ hours. In what time can B copy $$42$$ pages?

Two pipes $$A$$ and $$B$$ can fill a cistern in $$37\displaystyle\frac{1}{2}$$ minutes and $$45\ minutes $$ respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the $$B$$ is turned off after :

A pump can fill a tank with water in $$2\ hours$$. Because of a leak, it took $$2\displaystyle\frac{1}{3}\ hours$$ to fill the tank. The leak can drain all the water of the tank in.

Which of the following is correct?

Two pipes P and Q would fill a cistern in $$24$$ and $$32$$ minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in $$16$$ minutes

A cistern has a leak which would empty it in $$8$$ hours. A tap is turned on which admits $$6$$ litres a minute into the cistern and is now emptied in $$12$$ hours. How many litres does the cistern hold?