Quantitative Aptitude

Time, Work, and Projects

198 Questions

Time and work questions test the ability to calculate the time required to complete tasks involving individual or combined worker efficiency. These problems frequently appear in competitive exams to assess logical calculation skills. Topics include pipes, cisterns, group efficiency, and hourly work rates.

Combined work efficiencyMen and days calculationsWorker efficiency ratiosWorking hours per dayLeaving and joining workers

Time, Work, and Projects Questions

Multiple choice maths how much does it weigh? basic operations with same units operations involving units of length calculations define weight and units of weight

Mr Sahoo attended a 1-day workshop from 09:15 a.m. to half five in the evening. The workshop included a $1\frac{1}{4}$ hour lunch break, two 15 minutes tea breaks and 13 activities, each of equal duration. Calculate the duration of each activity.

  1. $30$ minutes
  2. $20$ minutes
  3. $25$ minutes
  4. $40$ minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total time of the workshop =$8$ hours and $15$ min

$=8 \times 60+15=495 $ min

Total time of tea break = $30$ min

lunch break time = $75$ min

hence time available for 13 activities 
$=495-75-30$ $=6$ hours and $30$ min
$=390 $ min

So, time devoted to each activity $=\dfrac{390}{13}=30$ min

Multiple choice political science gender inequality across the wall gender disparity global problems and india's role human rights : origin, characteristics and types international problems problems affecting the world

How much more an Indian woman, on an average, works than a man every day?

  1. one hour more

  2. two hours more

  3. three hours more

  4. one hour less
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
 On an average, an Indian woman works one hour more than an average man every day. Yet much of her work is not paid and therefore often not valued. 
Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

The number of workers increased the days to complete the work decreased."is example of 

  1. Inverse ratio

  2. Direct ratio

  3. Both of A and B

  4. none of above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Inverse proportion is a relation between two quantities such that one increases in proportion as the other decreases i.e. If $x$ increases as $y$ decreases, $x \alpha \dfrac{1}{y}$ 

In the given example, if the no. of workers are increased then the time required to do the job will decrease, likewise if no. of workers decrease, then time to do the same job will increase i.e. no. of workers and time to do job are inversely proportional to each other.
hence the answer is inverse proportion
So, the answer is option A.

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

Ten men, working for 6 days of 10 hours each, finish $ \dfrac {5}{21} $ of a piece of work. How many men working at the same rate and for the same number of hours each day, will be required to complete the remaining work in 8 days?

  1. 24

  2. 26

  3. 25

  4. 21
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Lets first find the number of working hours required to complete $\dfrac { 5 }{ 21 }$ of the work.
M = number of men
D = number of days
H = number of hours worked per day
N = work done
MDH = N
10$\times $6$\times $10 = $\dfrac { 5 }{ 21 }$
600 hours to complete $\dfrac { 5 }{ 21 }$ of work
Let the total number of hours required to complete the work be $x$ then
$x$ = $\dfrac { 5 }{ 21 }$ $\div $600
   = 600$\times $$\dfrac { 21 }{ 5
 }$
$x$   = 2520 hours
so the remaining work is $x$$-$  $\dfrac { 5 }{ 21 }$
               = $\dfrac {16 }{ 21 }$ $x$

               =$\dfrac {16 }{ 21 }$$\times $2520
               = 1920 hours required to complete remaining $\dfrac {16 }{ 21 }$ of the work
 now the equation we get is
MDH = N
MDH = 1920
M $\times $ 8$\times $10 = 1920
M =  $\dfrac { 1920 }{ 80 } $
M = 24
 Ans. 24 men

Multiple choice maths profit-loss overhead expenses introduction to total cost price of the article profit and loss with overhead expenses

if 5 men and 9 women can do a piece of work in 19 days then in how many days will 3 men and 6 women do the same work ?

  1. 12 days

  2. 15 days

  3. 18 days

  4. 21 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
It is given that 5 men or 9 women can do the job in 19 days.

So, 5 men=9 women

1 man = $\dfrac { 9 }{ 5 }$ women

3 men = 3 $(\dfrac { 9 }{ 5 } )$ women

So, work done = 3 men+6 women = 3 $(\dfrac { 9 }{ 5 } )+6$

$=\dfrac { 27 }{ 5 } +6$

$=\dfrac { 57 }{ 5 } $

Now,$ \dfrac { {M} _{1} {D} _{1} }{{W} _{1} }$= $ \dfrac { {M} _{2} {D} _{2} }{ {W} _{2} } ,$ 

let ${D} _{2} = x$

$\dfrac { 9*19 }{ {W} _{1} } = \dfrac { \dfrac { 57 }{ 5 } *x }{ {W} _{2} }$

$ \Longrightarrow 9*19=\dfrac { 57x }{ 5 }$

$ \Longrightarrow 3=\dfrac { x }{ 5 }$

$ \Longrightarrow x=15$ days

So, option (b) is correct.
Multiple choice introduction to ratio and percentages comparing quantities maths

36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?

  1. 12

  2. 18

  3. 22

  4. 24

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the required number of days be x.
Less men, More days (Indirect Proportion)
$\therefore 27 : 36 :: 18 : x \Leftrightarrow 27 \times x = 36 \times 18$
$\Rightarrow x = \dfrac{36 \times 18}{27}$
$\Rightarrow x = 24$

Multiple choice introduction to ratio and percentages comparing quantities maths

Ravi and Kumar are working on as assignment. Ravi takes $6$ hours to type $32$ pages on a computer, while Kumar takes $5$ hours to type $40$ pages. How much time will they take, working together on two difference computers to type an assignment of $110$ pages?

  1. $7$ hours $30$ minutes
  2. $8$ hours
  3. $8$ hours $15$ minutes
  4. $8$ hours $25$ minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Number of pages typed Rave in $1$ hour $=\cfrac{32}{6}=\cfrac{16}{3}$
Number of pages typed by Kumar in $1$ hour $=\cfrac{40}{5}=8$.
Number of pages typed by both in $1$ hour $=\left( \cfrac { 16 }{ 3 } +8 \right) =\cfrac { 40 }{ 3 } $.
$\therefore$ Time taken by both to type $110$ pages $=\left( 110\times \cfrac { 3 }{ 40 }  \right) $ hours
$=8\cfrac{1}{4}$ hours (or) $8$ hours $15$ minutes.

Multiple choice introduction to ratio and percentages comparing quantities maths

Sakshi can do a piece of work in $20$ days. Tanya is $25$% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

  1. $15$
  2. $16$
  3. $18$
  4. $25$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ratio of times taken by Sakshi and Tany $=125:100=5:4$.
Suppose Tanya takes $x$ days to do the work.
$5:4::20:x$ $\Rightarrow \left( \cfrac { 5\times 20 }{ 5 }  \right) $
$\Rightarrow$ $x=16$ days.
Hence, Tanya takes $16$ days to complete the work.

Multiple choice maths direct proportion and inverse proportion rule of three types of proportions direct proportion

$A$ can do a piece of work in $10$ days and $B$ in $15$ days. How long will they take together to finish it ? 

  1. $7$ days
  2. $3$ days
  3. $9$ days
  4. $6$ days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work done by A in 1 day $=\dfrac{1}{10}$


Work done by B in 1 day$=\dfrac{1}{15}$

Work done by A and B in 1 day$=\dfrac{1}{10}+\dfrac{1}{15}=\dfrac{25}{150}$

Working together they will complete the work in $\dfrac{150}{25}=6$ days

Multiple choice maths direct proportion and inverse proportion rule of three types of proportions direct proportion

$A, B$ and $C$ can finish a job working alone in $72, 24$ and $36$ days respectively. In how many days they can finish the job if they worked together?

  1. $12$
  2. $9$
  3. $15$
  4. $18$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the total work be $72$ units (LCM on $72, 24$ and $36$).


$A, B$ and $C's$ one day work is $1, 3$ and $2$ units respectively.

Required number of days $= \dfrac {72}{6} = 12$.


Alternate method
$(A+B+C)'s$ one day work =$\dfrac{1}{72}+\dfrac{1}{24}+\dfrac{1}{36}$

$=\dfrac{1+2+3}{72}=\dfrac{6}{72}$

Number of days required $= \dfrac {72}{6} = 12$ days to finish the work when 3 of them work together.

Multiple choice applications of quadratic equations solving (simple) problems word problems based on quadratic equations quadratic equation maths

For the same amount of work , A takes 6 hours less than B. If together they complete the work in 13 hours 20 minutes; find how much time will B alone take to complete the work.

  1. $20$ hrs
  2. $30$ hrs
  3. $10$ hrs

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the time taken to complete the work  by B be  x.
A can take x - 6 hours.

A and B together can complete the work = 13 hours 20 minutes.
$\frac{1}{x-6}+\frac{1}{x}=13\frac{20}{60}$
$\frac{2x-6}{x^2-6x}=\frac{3}{40}$
$40(2x-6)=3x^2-18x$
$80x-240=3x^2-18x$
$3x^2-98x+240$
Using quadratic formula,
$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$\frac{98\pm\sqrt{(-98)^2-4\times 3\times 240}}{2\times 3}$
$\frac{98\pm\sqrt{6724}}{6}$
$\frac{98\pm 82}{6}$
So, x = 30, x = 2.6666..
x value cannot be negative.
B take 30 hours to complete the work alone.

Multiple choice applications of quadratic equations solving (simple) problems word problems based on quadratic equations quadratic equation maths

 A can do a piece of work in $'x'$ days and $B$ can do the same work in $'x+16'$ days.If both working together can do it in $15$ days. Calculate $x$.

  1. $24$
  2. $25$
  3. $27$
  4. $None\ of\ the\ above$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given A do a piece of work in x days and B do work in x+16 days

Then A one day work = $\frac{1}{x}$ days
AND B one day work =$\frac{1}{x+16}$days
Then Both one day work =$\frac{1}{x}+\frac{1}{x+16}=\frac{x+16+x}{x(x+16)}=\frac{2x+16}{x^{2}+16x}$ 
So both do work in $\frac{x^{2}+16x}{2x+16} \ days$ 
But both do work in 15 days
$\therefore \frac{x^{2}+16x}{2x+16}=15$
$\Rightarrow x^{2}+16x=30x+240$
$\Rightarrow x^{2}-14x-240=0$
$\Rightarrow x^{2}-24x+10x-240=0$
$\Rightarrow x(x-24)+10(x-24)=0$
$\Rightarrow (x-24)(x+10)=0$
Then $x-24=0 , x=24$
And $x+10=0 , x=-10$
But work done is not negative
Then work done =$24$ days