Quantitative Aptitude

Time, Work, and Projects

190 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 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

Multiple choice exponent of a prime in n! factorial notation combinatorics and mathematical induction permutations and combinations maths

'$X$' completes a job in $2$ days and '$Y$' completes it in $3$ days and '$Z$' takes $4$ days to complete it. If they work together and get Rs. $3,900$ for the job, then how much amount does '$Y$' get?

  1. Rs. $1,800$
  2. Rs. $ 1,200$
  3. Rs. $ 900$
  4. Rs. $ 800$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$X$ do job in $2$ days, $Y$ completes it in $3$ days, $Z$ takes $4$ days.
If $X, Y, Z$ together can do in $1$ day, then 
$= \dfrac {1}{2} + \dfrac {1}{3} + \dfrac {1}{4} = \dfrac {13}{12}$ of work
Therefore, the whole work is done in $\dfrac {12}{13}$ of a day.
Daily wages of $Y = \dfrac {1}{3}\times $ Rs. $ 3,900 =$ Rs. $ 1,300$
$\therefore$ Amount of $Y = \dfrac {12}{13} \times$ Rs. $ 1,300 =$ Rs. $1,200$

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

Rehna works $2\cfrac { 1 }{ 2 } $ hours each day on her embroidery. She completes the work in $7$ days. How many hours did she take to complete her work?


Ans : $17\cfrac { 1 }{ 2 } $ hrs.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rehana works $2\dfrac{1}{2}$ hrs $= 150 $minutes


As she completed her work in $7$ days,

$150 \times 7 = 1050$ minutes = $\dfrac{1050}{60}$ hours

$=\dfrac{35}{2}$ hours $=17\dfrac{1}{2}$ hours


So, Rehana took $17\dfrac{1}{2}$ hours to complete her work.

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

Deepak can paint $\cfrac { 2 }{ 5 } $ of a house in one day. If he continuous working at this rate, how many days will he take to paint the whole house?

  1. $2\cfrac { 1 }{ 2 } $ days
  2. $1\cfrac { 1 }{ 2 } $ days
  3. $\cfrac { 1 }{ 2 } $ days
  4. $2\cfrac { 1 }{ 4 } $ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\boxed{\text{Work(W)}\propto \text{Days(D)}\\dfrac{W _1}{D _1}=\dfrac{W _2}{D _2}}$

given,
$W _1=\dfrac25\quad D _1=1\,\text{day}\W _2=1\,\,\text{(painting the whole house)}$
to find, $D _2=?$

$\dfrac{2/5}{1}=\dfrac{1}{D _2}\Rightarrow D _2=\dfrac52$

$\therefore D _2=2\dfrac12 \,\text{days}$

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

A can do a piece of work in $24$ days. If B is $60\%$ more efficient then the number of days required by B to do the twice as large as the earlier work is-

  1. $24$
  2. $36$
  3. $15$
  4. $30$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
According to the question-
A can do a piece of work in $24$ days.
$\therefore$ work done by A in $1$ day  $=\cfrac{1}{24}$
Given that, B is $60 \%$ more efficient, i.e., B can do $60 \%$ more work than work done by A in $1$ day-
Work done by B in $1$ day  $=\cfrac{1}{24} + \cfrac{60}{100} \times {1}{24} = \cfrac{1}{15}$
$\therefore$ number of days required by B to do the same work $= 15 $days
$\therefore$ number of days required by B to do the twice as large as the earlier work  $=2 \times 15 = 30$ days
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

A and B can do a job in $12$ days, B and C can do it in $16$ days. After A has worked for $5$ days and B has worked for $7$ days, C can finish the rest in $13$ days. In how many days can C do the work alone?

  1. $16$ days
  2. $24$ days
  3. $36$ days
  4. $48$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solution:-

Let the amount of work done by $A, B,$ and $C$ per day be $x, y$ and $z$ respectively.
Case I:-

$A$ and $B$ can do the job in $12$ days.
$\therefore$ work done by $A$ and $B$ in one day  $=\cfrac{1}{12}$
$\Rightarrow \; x + y = \cfrac{1}{12}$
Case II:-
B and C can do the job in $16$ days.
$\therefore$ work done by B and C in one day  $=\cfrac{1}{16}$
$\Rightarrow \; y + z = \cfrac{1}{16}$
As given, A has worked for $5$ days and B has worked for $7$ days, C can finish the rest in $13$ days.
$5x + 7y + 13z = 1$
$\Rightarrow$ $5x + 5y + 2y + 2z + 11z = 1$
$\Rightarrow$ $5(x + y) + 2(y + z) + 11z = 1$
$\Rightarrow \; 5 \times \cfrac{1}{12} + 2 \times \cfrac{1}{16} + 11z = 1$
$\Rightarrow \; 11z = 1 - \cfrac{5}{12} - \cfrac{1}{8}$
$\Rightarrow \; 11z = \cfrac{22}{48}$
$\Rightarrow \; z = \cfrac{1}{24}$
Therefore, work done by $C$  $1$ day  $=\cfrac{1}{24}$
Hence, C alone can finish the work in $24$ days.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

If $12$ men complete a work in $20$ days. If only $8$ men are  employed, then the time required  to complete  the same work is

  1. $24$ days
  2. $25$ days
  3. $30$ days
  4. $35$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

As $12$ men complete work in $20$ days, $1$ man will complete the same work in

$20\times12=240$ days.

Time required by $8$ men to complete the work=$\dfrac{240}{8}$=$30$ days..

Multiple choice economics employment: growth, informalisation and other issues measures to alleviate unemployment unemployment measures unemployment and employment generation

A person working for 8 hours a day for _______  of the year is regarded as employed on a standard person year basis.

  1. 300 days

  2. 365 days

  3. 273 days

  4. 333 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In Indian labor statistics, a person is considered employed on a Standard Person Year (SPY) basis if they work for 273 days of 8 hours each in a year.