Numerical Appli...

The average of statistical data is called :

Two men and $$5$$  boys together can finish a piece of work in  $$4$$ days, while $$3 $$ men and $$ 6$$  boys can finish in $$3$$  days. Find the time taken :
(i) by one man alone to finish the work
(ii) by one boy alone to finish the work.

A contractor undertakes to dig a canal, $$6$$ kilometers long in $$35$$ days and employed $$90$$ men. He finds that after $$20$$ days only $$2$$ km of canal have been completed . How many more men must be employed to finish the work in time?

Pooja and Ritu can do a piece of work in $$17\displaystyle \frac{1}{7}$$ days. If one day work of Pooja be three fourth of one day work of Ritu; find in how many days each alone will do the work.

A cabinet of ministers consists of 11 ministers, one minister being the chief minister. A meeting is to be held in a room having a round table and 11 chairsround it, one of them being meant for the chairman. The number of ways in which the ministers can take their chairs, the chief minister occupying the chairman's place, is

$$16$$ men can complete a work in $$12$$ days, $$24$$ children can complete the same work in $$18$$ days, $$12$$ men and $$8$$ children started working and after $$8$$ days, $$3$$ more children joined them. How many days will they now take to complete the remaining work ?

A particular work can be completed by $$6$$ men and $$6$$ women in $$24$$ days, whereas the same work can be completed by $$8$$ men and $$12$$ women in $$15$$ days. Find the time taken by $$4$$ men and $$6$$ women to complete the same work .

$$A$$ and $$B$$ can do a piece of work in $$5$$ days, $$B$$ and $$C$$ can do it in $$7$$ days. $$A$$ and $$C$$ can do it in $$4$$ days. Who among these will take the least time if put to do it alone ?

A and B can do a job in $$12$$ days, B and C can do it in $$16$$ days. After A has worked for $$5$$ days and B has worked for $$7$$ days, C can finish the rest in $$13$$ days. In how many days, can C do the work alone?

$$3$$ men and $$4$$ boys can do a piece of work in $$14$$ days, while $$4$$ men and $$6$$ boys do the same work in $$10$$ days. How long would it take one man to finish the same work ?