TNPSC – TIME AND WORK

TNPSC – TIME AND WORK

Time and Work:

In this chapter we will cover the following two topics they are based on similar concepts.

(i) Time and Work

(ii) Pipes and Cisterns

==> Work is the job assigned or job completed. The rate of work is the speed or speed of work.

Quick method:

If a person completes a job in n days then he will complete 1/n ^th part in one day.

==> A is twice as good a work man as B, then he will finish the work in half the time.

==> If A and B can do a piece of work in X and Y days respectively while working alone, they will together take (xy) / (x+y) days to complete it.

==> If A, B, C can do a piece of work in X, Y, Z days respectively while working alone, they will together take (xyz) / [xy+yz+zx] days to finish it.

==> If A can finish a work in x days and B in y days and A, B and C together in s day then:

              C can finish the work alone in sxy / (xy-sy-yx)

              B+C can finish sx / (x*s) and

              A+C can finish in sy / (y-s)

PIPES AND CISTERNS

Pipes and cisterns problems use the same principles as of time and work. Here a piece connected with a cistern is called an inlet pipe to fill it or an outlet pipe to empty it.

Quick method:

==> If an inlet pipe can fill a cistern in A hours, the part filled in 1 hour = 1/A (same as work and time fundamentals)

==> If pipe A is ‘x’ times bigger than pipe B, then pipe A will take 1/x^th of the time taken by pipe B to fill the cistern.

==> If an inlet pipe can fill a tank in a hours and an outlet pipe empties the full tank in b hours, then the net part filled in 1 hour when both the pipes are opened = (1/a) – (1/b)

In 1 hour, the part filled (or emptied) = (1/a) – (1/b)

Time required to fill or empty the tank = (ab) / (b+a) hours.

==> If x and y fill/empty a cistern in ‘m’ and ‘n’ hours, then together they will take (mn) / (m+n) hours to fill/empty the cistern

And in one hour (n+m) / nm^th part of the cistern will be filled / emptied. (same as time and work)

==> If an inlet pipe fills a cistern in ‘a’ minutes and takes ‘x’ minutes longer to fill the cistern due to a leak in the cistern, then the time in which the leak will empty the cistern is

              a [1+ (a/x)]