# Aptitude Time and Work

Two quantities are said to be directly related. If one quantity increases the other quantity also increases.

** Example**: Men and Work

Two quantities are said to be inversely related if one quantity increases the other quantity decreases

** Example**: Men and Time

**Note:**

If there is more than one person carrying out the work then it is assumed that each person does same amount of work on each day i.e. capacity of every individual is equal.

M =Number of men

D =Number of days

H =Number of Hours

W =Work done

Work to be done is usually considered as one unit.

If a man can do a work in 6 days then in one day he will be able to do I part out of total 6 parts of work and conversely if he can do 1/8th part of the work in 1 day then he will be able to do the total work in 8 days.

6 days 1 work

1 day 1/6 work

If a tap can fill a tank in 30 minutes then in one minute it can fill 1/30th part of the tank and conversely if a tap can fill 1/8th part of the tank in 1 minute then it can fill the tank in 8 minutes

If 2 men together can do the work in 15 days it means that one man can do it in days [since men and time are inversely related]. This in turn means each person can do —1/30th of the work per day

If a boy can work three times as fast as a girl then the boy takes one third of the time the girl takes to complete the work.

If the girl takes 15 days to complete the work then the boy takes 5 days to complete the work. [Since efficiency and time are inversely related]

In pipes and cisterns a filling pipe does positive work and an emptying pipe or a leak does negative work.

Wages are to be distributed according to the work done by each person involved in the work (or). It can be divided in the ratio of their capacities (one day's work). If they work for the same time.

## IMPORTANT FORMULAS:

(i) If A can do a piece of work in X days and B can do the same work in Y days, then both of them working together will do the same work in

XY
/
X+Y

days .

(ii) A,B,C while working alone can complete a work X,Y and Z days respectively then they will together complete the work in

XYZ
/
XY+YZ+ZX