Time and work : Shortcuts. Basic Formulas and Tricks,

Time and work is one topic that is every aptitude test whether its a competitive exam or any college entrance exam or any job aptitude tests.

So in this article, we will help you with the basic formulas shortcuts, and tricks so you can solve problems from this topic with minimum time and with accuracy.

Many companies such as TCS, Infosys, Wipro, Accenture, HCL, IBM have their aptitude exams and question from this topic.

Questions in this section which asked in entrance exams are more advanced and more complicated but they can be solved with ease if you know the basic formulas, tricks, and shortcuts.

Basic Concepts of Time and Work:

As we learned in our high school about the basic correlation between time, work, and man-hours, if you remember those concepts then you can solve most of the aptitude questions on this topic.

The analogy between problems on time and work to time, distance, and speed:
1. Speed is equivalent to the rate at which work is done
2. Distance traveled is equivalent to work done.
3. Time to travel distance is equivalent to time to do work.

Man – Work – Hour Formula:
More men can do more work.
More work means more time required to do work.
More men can do more work in less time.
$M$ men can do a piece of work in $T$ hours then,

Total effort or work = MT man-hours.

$Rate of work * Time = Work Done$

$Rate of work * Time = Work Done$ If $A$ can do a piece of work in $D$ days then,

$A$ ‘s 1 day’s work = $\frac{1}{D}$ .
Part of the work done by $A$ for $t$ days = $\frac{t}{D}$

If $A$ ‘s 1 day’s work = $\frac{1}{D}$ can finish the work in $D$ days.

$\frac{M D H}{W} = Constant$

Where,

M = Number of men
D = Number of days
H = Number of hours per day
W = Amount of work

If $M_{1}$ men can do $W_{1}$ work in $D_{1}$ days working $H_{1}$ hours per day and $M_{2}$ men can do $W_{2}$ work in $D_{2}$ days working $H_{2}$ hours per day, then

$\frac{M_{1} D_{1} H_{1}}{W_{1}} = \frac{M_{2} D_{2} H_{2}}{W_{2}}$

If $A$ is $x$ times as good a workman as $B$ , then:

The ratio of work done by $A$ and $B$ = $x : 1$

The ratio of times taken by $A$ and $B$ to finish a work = $1 : x$ i.e. $A$ will take ${(\frac{1}{x})}^{t h}$ of the time taken by $B$ to do the same work.

Shortcuts :

$A$ and $B$ can do a piece of work in $' a'$ days and $' b'$ days respectively, then working together:
They will complete the work in $\frac{a b}{a + b}$ days
In one day, they will finish { ${(\frac{a + b}{a b})}^{t h}$ part of work.

If A can do a piece of work in a days, $B$ can do in $b$ days and $C$ can do in $c$ days then,

A, B and C together can finish the same work in \frac{a b c}{a b + b c + c a} days

If $A$ can do a work in $x$ days and $A$ and $B$ together can do the same work in $y$ days then,

Number of days required to complete the work if B works alone = \frac{x y}{x - y} d a y s

If $A$ and $B$ together can do a piece of work in $x$ days, $B$ and $C$ together can do it in $y$ days, and $C$ and $A$ together can do it in $z$ days, then the number of days required to do the same work:

If A, B, and C working together = $\frac{2 x y z}{x y + y z + z x}$

If A working alone = $\frac{2 x y z}{x y + y z - z x}$

If B working alone = $\frac{2 x y z}{- x y + y z + z x}$

If C working alone = $\frac{2 x y z}{x y - y z + z x}$

If $A$ and $B$ can together complete a job in $x$ days.
If $A$ alone does the work and takes $a$ days more than $A$ and $B$ working together.
If $B$ alone does the work and takes $b$ days more than $A$ and $B$ working together.

Then, $x = \sqrt{a b} days$

If $m_{1}$ men or $b_{1}$ boys can complete a work in $D$ days, then $m_{2}$ men and $b_{2}$ boys can complete the same work in

$\frac{D m_{1} b_{1}}{m_{2} b_{1} + m_{1} b_{2}}$ ays.

If $m$ men or $w$ women or $b$ boys can do work in $D$ days, then 1 man, 1 woman, and 1 boy together can do the same work in

$\frac{D m w b}{m w + w b + b m}$ days

If the number of men to do a job is changed in the ratio $a : b$ , then the time required to do the work will be changed in the inverse ratio. ie; $b : a$

If people work for the same number of days, the ratio in which the total money earned has to be shared is the ratio of work done per day by each one of them.
$A$ , $B$ , $C$ can do a piece of work in $x$ , $y$ , $z$ days respectively. The ratio in which the amount earned should be shared is $\frac{1}{x} : \frac{1}{y} : \frac{1}{z} = y z : z x : x y$

If people work for a different number of days, the ratio in which the total money earned has to be shared is the ratio of work done by each one of them.

The Most Common Questions Asked :

A takes x days to do work. B takes y days to do the same work. If A and B work together, how many days will it take to complete the work?
If A and B together can do a piece of work in x days, B and C together can do it in y days, and C and A together can do it in z days, find how many days it takes for each of them to complete the work if they worked individually. How many days will it take to complete the work if they worked together?
Give A is n times efficient than B. Also A takes n days less than B to complete the work. How many days will it take to complete the work if they worked together?
Problem 5 with 3 people joining work one after the other.
Given A takes x days to do work. B takes y days to do the same work. If A and B work on alternate days ie A alone works on the first day, B alone works on the next day, and this cycle continues, in how many days will the work be finished
Problems related to wages from work. How much each person earns from the work done.
Problems where combinations of workers [men, women, girls, and boys take some days to do a job. These problems are solved using man-days concept.

Time And Work : Formula, Tricks and Shortcuts

Basic Concepts of Time and Work:

Shortcuts :

The Most Common Questions Asked :

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