Time & Work Topic-Wise Short Notes, Solutions, Methods, Tips, Tricks & Techniques To Solve Problems

Time and Work - Basic Formulas, Shortcuts, Rules, Tricks & Tips - Quantitative Aptitude

Useful For All Competitive Exams Like UPSC, SSC, BANK & RAILWAY

Posted By Careericons Team

Introduction to Time and Work:

Time and Work is an important topics for every aptitude test. This topic plays an important role in all competitive exams and other equivalent aptitude tests, on average 4 to 6 questions from this topic are regularly asked in BANK, SSC, UPSC, etc.

The questions from this Time and Work are not directly based on formulae. For solving the questions of this, concepts of ratio and proportion are required. Students & Candidates are advised to be highly attentive in solving the problems of these topics.

Time and work deal with the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the work done by each of them.

Something that one does as part of one’s regular work may consist of many small tasks or a large one. But the work is always to be completed in a given period of time. To complete the given task earlier one has to increase the number of persons engaged in doing that task or vice versa.

While dealing with problems with wages, it may be kept in mind that the money obtained is always divided by the ratio of the work done by each person and for how much time. In time and work problems, three items are involved: the number of people working, the time, and the amount of work done.

  • The number of people working is directly proportional to the amount of work done, i.e., the more people on the job, the more work that will be done, and vice versa.
  • The number of people working is inversely proportional to the time, i.e., the more people on the job, the less time it will take to finish the job, and vice versa.
  • The time spent on the work is directly proportional to the amount of work done; i.e., more time spent, more work done, and vice versa.

Pipe and cistern or tank problems are similar to time and work problems. Completely filling (or emptying) a tank may be thought of as completing a job. Also check the link provided to learn Pipes & Cistern type of problems.


Basic Time & Work - Types, Concepts, Tricks, & Shorcut PDF

Basically, Time is the duration taken during any activity or work that has been done/ completed or in process/ still working. And Work is the assigned task or a set of activities to achieve a specific result.

Here we list out some of the basic types of questions which are asked in the various exam with respect to the time and work topic:

Type 1. To find the efficiency of a person with comparison to others work or efficency

Type 2. To find the time taken by an individual to do a piece or part of work

Type 3. To find the time taken by a group of individuals to complete a piece or part of work

Type 4. Work done by an individual in a certain or specific or targeted time duration

Type 5. Work done by a group of individuals in a certain or specific or targeted time duration


Top "10" Concepts of Time and Work Aptitude Problems

In these questions topic, All the concepts are based on the time taken by one/two persons or groups in doing certain works. required number of persons for any work is commonly asked. Comparison of male, female, and children's works, time taken after distribution/change and questions based on efficiency (per cent of ratio) are also asked.

There are 10 basic Concepts based on Time and Work problems asked in various SSC, BANK, UPSC, Railway & other competitve exams. From learning these 10 concpets with formulas & examples you can solve all kinds of problems that you face in your upcoming examinations.

Note that 'time and work' and 'number of labour and work', have a direct ratio while 'time and number of labour' have inverse ratios to solve these questions use the ratio method be it is noted practice will ensure your accuracy and fast speed.

Lets see the time and work concepts one by one,

Concept 1:

(1) If a person can complete a work in 'D' days, then the work done by him in 1 day is $1/D$ Efficiency is inversely proportional to the time taken (T) when the work done is constant.

E α $1/T$

(2) If P is 'n' times more efficient than Q, than P will take $1/n$ time of the total time taken by Q to complete the same amount of work.


Concept 2:

If $M_1$ persons can do $W_1$ work in $D_1$ days working $H_1$ hours and $M_2$ person can do $W_2$ work in $D_2$ days working $H_2$ hours, then relation between them is

${M_1 D_1 H_1}/{W_1} = {M_2 D_2 H_2}/{W_2}$


Concept 3:

If A does a work in 'a' days and B in 'b' days then both can complete the work in ${ab}/{a+b}$ days.


Concept 4:

If A and B can complete a work in x days and A alone can finish that work in y days, then number of days B takes to complete the work is = ${xy}/{x-y}$ days.


Concept 5:

A, B, C can do a work in x, y and z days respectively. They will finish the work in ${xyz}/{xy+yz+zx}$ days


Concept 6:

If A and B can do a piece of work in x days, B and C can do the same work in y days and A and C can do it in z days, then, working together they can complete that work in ${2xyz}/{xy+yz+zx}$ days


Concept 7:

If A takes 'a' days more to complete a work than the time taken by (A+B) to do some work and B takes 'b' days more than the time taken by (A+B) to do same work.

Then, (A + B) do the work in $√{ab}$ days.


Concept 8:

A can do a certain piece of work in $d_1$ days and B in $d_2$ days. Then, the ratio of wages of A and B are:

A's share : B's share = $1/d_1 : 1/d_2 = d_2 : d_1$

A, B and C can do a piece of work in $d_1, d_2$ and $d_3$ days. Then the ratio of wages of A, B and C are

A's share : B's share = $1/d_1 : 1/d_2 : 1/d_2$

Multiplying each equation by ($d_1 d_2 d_3$) Then the ratio is

A's share : B's share : C's share = $d_2 d_3 : d_1 d_3 : d_1 d_2$


Concept 9:

If A, B and C can do a piece of work in x, y and z days respectively. The contract for the work is Rs. r and all of them work together.

Then, Share of A = Rs. $(\text"ryz"/\text"xy + yz + zx")$,

Share of B = Rs. $(\text"rzx"/\text"xy + yz + zx")$,

Share of C= Rs. $(\text"rxy"/\text"xy + yz + zx")$,


Concept 10:

A can do a piece of work in x days. With the help of B, A can do the same work in y days. If they get Rs. a for that work

Then, Share of A = Rs. $(\text"ay"/x)$

And Share of B = Rs. $(\text"a (x - y)"/x)$

By knowing these all concepts & formulas, You can completely find a link to a solution as soon as you read the question. Thus, not only knowing the formula you can solve any numerical ability topic & make the solution with the related calculations simpler & easier.


"27" - Important Aptitude Rules, Formulas & Quick Tricks to Solve Time & Work Based Aptitude Problems

In this list of rules, you will get an idea that How to solve all different types & kinds of Time & Work based aptitude problems asked in various competitive exams like UPSC, SSC, Bank, and Railway examinations at all levels.

By using this method, you can able to solve all problems from basic level to advanced level of questions asked based on Time and Work in a faster approch.

Let's discuss the rules one by one with all Time and Work related formulas with examples,

RULE 1 :

If $M_1$ men can finish $W_1$ work in $D_1$ days and $M_2$ men can finish $W_2$ work in $D_2$ days then, Relation is

$\text"M_1D_1"/ \text"W_1" = \text"M_2D_2"/ \text"W_2"$

And If $M_1$ men finish $W_1$ work in $D_1$ days, working $T_1$ time each day and $M_2$ men finish $W_2$ work in $D_2$ days, working $T_2$ time each day, then

$\text"M_1D_1T_1"/ \text"W_1" = \text"M_2D_2T_2"/ \text"W_2"$


RULE 2 :

If A completes a piece of work in 'x' days, and B completes the same work in 'y' days, then,

Work done by A in 1 day = $1/x$, Work done by B in 1 day = $1/y$

Work done by A and B in 1 day = $1/x + 1/y = {x + y}/{xy}$

Total time taken to complete the work by A and B both = $({xy}/{x + y})$


RULE 3 :

If A can do a work in 'x' days, B can do the same work in 'y' days, C can do the same work in 'z' days then,

Total time taken by A, B and C to complete the work together

= $1/{1/x + 1/y + 1/z} = {xyz}/{xy + yz + zx}$and

If workers are more than 3 then total time taken by A, B, C ...... so on to complete the work together = $1/{1/x + 1/y + 1/z + ...}$


RULE 4 :

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

B alone can do the same work in $({xy}/{x - y})$ days.


RULE 5 :

If A and B can do a work in 'x' days, B and C can do the same work in 'y' days, C and A can do the same work in 'z' days. Then

Total time taken, when A, B and C work together

=$2/{(1/x + 1/y + 1/z)}$ OR ${2xyz}/{xy + yz + zx}$ days


RULE 6 :

Work of one day = $\text"Total work"/\text"Total no of working days"$

Total work = (work of one day) × (total no. of working days)

Remaining work = 1 – (work done)

Work done by A

= (Work done in 1 day by A) × (total no.of days worked by A,B and C and so on)

=${1/x}/(1/x + 1/y + 1/z + ...)$

where A can complete work in x days, B in y days, C in z days and so on....


RULE 7 :

If A can finish $m/n$ part of the work in D days.Then,

Total time taken to finish the work by

A = $D/({m/n}) = n/m $ × D days


RULE 8 :

(i) If A can do a work in 'x' days and B can do the same work in 'y' days and when they started working together, B left the work 'm' days before completion then

Total time taken to complete work is = $({y + m}/{x + y})x$

(ii) A leaves the work 'm' days before its completion then

Total time taken to complete work is = $({x + m}/{x + y})y$


RULE 9 :

If A and B together can finish a certain work in 'a' days. They worked together for 'b' days and then 'B'(or A) left the work. A (or B) finished the rest work in 'd' days, then

Total time taken by A (or B) alone to complete the work

= $\text"ad"/ \text"a – b"$ or $\text"bd"/ \text"a – b"$ days


RULE 10 :

If food is available for 'a' days for 'A' men at a certain place and after 'b' days. 'B' men join, then the remaining food will serve total men for

Required time = ${A(a – b)}/{(A + B)}$ days

If food is available for 'a' days for 'A' men at a certain place, and after 'b' days 'B' men leave then the remaining food will serve remaining men for

Required time = ${A(a – b)}/{(A - B)}$ days


RULE 11 :

If $A_1$ men and $B_1$ boys can do a certain work in $D_1$ days, Again, $A_2$ men and $B_2$ boys can do the same work in $D_2$ days, then, $A_3$ men and $B_3$ boys can do the same work in

Required time = ${D_1D_2(A_1B_2 – A_2B_1)}/{D_1(A_1B_3 – A_3B_1) - D_2(A_2B_3 – A_3 B_2)}$ days


RULE 12 :

If A men or B boys can do a certain work in 'a' days, then A1 men and B1 boys can do the same work in

Time taken = $a/{A_1/A + B_1/B} = {a(A . B)}/{A_1B + B_1A}$ days


RULE 13 :

If A men or B boys or C women can do a certain work in 'a' days, then $A_1$ men, $B_1$ boys and $C_1$ women can do the same work in

Time taken = $a/{A_1/A + B_1/B + C_1/C}$


RULE 14 :

If 'A' men can do a certain work in 'a' days and 'B' women can do the same work in 'b' days, then the total time taken when A1 men and B1 women work together is

Time taken = $1/{A_1/{A . a} + B_1/{B . b}}$

If A men do a certain work in 'a' days, B women do the same work in 'b' days and C boys do the same work in 'c' days then the total time taken when A1 men, B1 women and C1 boys can work together is

Total time taken = $1/{(A_1/{A . a} + B_1/{B . b} + C_1/{C . c})}$


RULE 15 :

The comparison of rate of work done is called efficiency of doing work.

Efficiency (E) $1/\text"No. of days"$ E1 : E2 : E3

= $1/D_1 : 1/D_2 : 1/D_3$,

E =$k/D$ or,

ED =k or, $E_1D_1= E_2D_2$


RULE 16 :

If the efficiency to work of A is twice the efficiency to work of B, then,

A:B (efficiency) = 2x:x and

A:B (time) = t:2t


RULE 17 :

If A can do a work in 'x' days and B is R% more efficient than A, then

'B' alone will do the same work in $x × 100/{100 + R}$ days


RULE 18 :

A, B and C can do a certain work together within 'x' days. While, any two of them can do the same work separately in 'y' and 'z' days, then in how many days can 3rd do the same work?

Required time = ${xyz}/{yz – x(y + z)}$days


RULE 19 :

A and B can do a work in 'x' days, B and C can do the same work in 'y' days. C and A can do the same work in 'z' days. Then, all can do alone the work as following:

A alone can do in =${2xyz}/{xy + yz - zx}$days

B alone can do in =${2xyz}/{-xy + yz + zx}$days

C alone can do in =${2xyz}/{xy - yz + zx}$days


RULE 20 :

A can do a certain work in 'm' days and B can do the same work in 'n' days. They worked together for 'P' days and after this A left the work, then in how many days did B alone do the rest of work ?

Required time = ${mn - P(m + n)}/m$ days

when after 'P' days B left the work, then in how many days did A alone do the rest of work?

Required time = ${mn - P(m + n)}/n$ days


RULE 21 :

If a man can do a certain work in 'd1' daysworking 'h1' hours in a days, while another man can do the same work in 'd2' days working 'h2' hours in a day. Whenthey work together everyday 'h' hours, then in how many days work will complete?

Required time = $[{({h_1d_1}) × ({h_2d_2})}/{h_1d_1 + h_2d_2}] 1/h$


RULE 22 :

The efficiency of A to work is 'n' times more than that of B, Both start to work together and finish it in 'D' days. Then,

A and B will separately complete, the work in

$({n + 1}/n)$D and (n + 1) D days respectively.


RULE 23 :

Some people finish a certain work in 'D' days. If there were 'a' less people, then the work would be completed in 'd'days more, what was the number of people initially?

Required number = $\text"a(D - d)"/\text"d"$ people


RULE 24 :

A can do a work in 'm' days and B can do the same work in 'n' days. If they work together and total wages is R, then.

Part of A = $n/{m + n} × R$

Part of B = $m/{m + n} × R$


RULE 25 :

If A, B and C finish the work in m, n and p days respectively and they receive the total wages R, then

The ratio of their wages is $1/m : 1/n : 1/p$


RULE 26 :

A and B can do a piece of work in x and y days, respectively. Both begin together but after some days.A leaves the job and B completed the remaining work in a days. After how many days did A leave?

Required time, t = $\text"(y - a)"/\text"(x + y)" × x$


RULE 27 :

If A men and B boys can complete a work in x days, while A, men and B, boys will complete the same work in y days, then

$\text"One day work of 1 man"/\text"One day work of 1 boy"$ = ${(yB_1 - xB)}/({xA - yA_1})$


7 - Types of Time and Work Based Aptitude Questions and Answers Practise Test With Online Quiz

Click the below links & Learn the specific model from Time and Work problems that you have to practice for upcoming examination


Refer: Get all Topic-wsie Quantitative aptitude problems for upcoming competitive exams

TIME & WORK MCQ QUESTION & ANSWER EXERCISE
time & work Shortcuts and Techniques with Examples

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