Numerical Appli...

A alone can do a piece in $$10$$ days and $$B$$ alone can so it in $$15$$ days. In how many days will $$A$$ and $$B$$ together do the same work?

$$20$$ persons are invited for a party, then the number of ways in which they and the host be seated at a round table is

The number of ways in which 7 persons can be arranged around a circle is:

A factory requires $$42$$ machines to produce a given number of articles in $$63$$ days. How many machines would be required to produce the same number of articles in $$54$$ days?

The mean of five numbers is $$30$$. If one number is excluded, their mean becomes $$28$$. The excluded number is:

Ten pipes of the same type can fill up a tank in $$16$$ minutes. If two pipes go out of order, how long will the remaining pipes take to fill the tank ?

Two persons could fit new windows in a house in $$3$$ days. One of the persons fell ill before the work started. How long days would the job take now?

If $$5$$ workers can build a fence in  $$65$$ days, how long would it take $$13$$ workers to build the same fence?

$$3$$  persons weave  $$168$$  shawls in $$14$$ days, how many shawls will 8 people weave in $$5 $$ days?

$$15$$ labourers can fill  $$35$$  boxes in  $$7$$  days. How many labourers can fill  $$65$$  boxes in $$5$$  days ?