Time and Work: Aptitude Questions with Solutions – Free Practice!
Welcome to our practice page dedicated to helping you ace Time and Work questions for placement aptitude tests!
Review Time and Work Concepts
Q. 1 Jack can complete a coding task in 10 hours. How much of the task will he finish in 4 hours?
Check Solution
Ans: D
Rate of work = 1/ 10
Total work done = (1/10) * 4 * 100 %
Q. 2 Two skilled workers, Aryan and Bhola, decide to take on a large task together. Aryan, with years of experience, can finish the job in 40 days, while the industrious Bhola can complete it in 30 days. They work together for 10 days when they realize they could use some extra help. Enter Chandru, who joins the team and helps them finish the remaining work in just 5 days. How long would it take Chandru to complete the entire work if left to do it alone?
Check Solution
Ans: A) 24 days
Total work = $( \text{LCM}(40, 30) = 120 )$ units. A and B’s rate = $( \frac{120}{40} + \frac{120}{30} = 3 + 4 = 7 )$ units/day. In 10 days, A and B do $( 10 \times 7 = 70 )$ units. Remaining work = $( 120 – 70 = 50 )$ units in 5 days. C’s rate = $( \frac{50}{5} = 10 )$ units/day, so C alone takes $( \frac{120}{10} = 24 )$ days.
Have a look at common Time and Work Scenarios.
Q. 3 10 women can complete a work in 15 days. Now, the deadline is suddenly shortened, and the work must be finished in just 5 days! How many women need to join the team to ensure the job is completed on time without compromising quality?
Check Solution
Ans: C) 30
Total work = $( 10 \times 15 = 150 )$ woman-days. Required number of women = $( \frac{150}{5} = 30 )$.
Q. 4 A and B form a small but effective team. Together, they can complete a project in just 12 days. However, if A were to work alone, it would take 20 days to finish the same task. How many days would it take for B to complete the project if they were to handle it single-handedly?
Check Solution
Ans: A) 30 days
Let total work be ( W ). A’s rate = $( \frac{W}{20} )$, and (A+B)’s rate = $( \frac{W}{12} )$. B’s rate = $( \frac{W}{12} – \frac{W}{20} = \frac{5W – 3W}{60} = \frac{2W}{60} = \frac{W}{30} )$. Thus, B alone can complete it in 30 days.
Q. 5 Aravind Construction Site employs two groups: men and women. In one instance, a team of 8 men and 6 women manages to finish a task in 10 days. In another scenario, 10 men and 8 women accomplish the same task in just 8 days. If 1 man and 1 woman were to work together without any additional help, how long would it take for them to complete the same task?
Check Solution
Ans: C) 80 days
Let 1 man’s work = ( x ) and 1 woman’s work = ( y ). $( 8x + 6y = \frac{1}{10} )$ and $( 10x + 8y = \frac{1}{8} )$. Solving, $( x + y = \frac{1}{80} )$, so they take 80 days together.
Q. 6 Worker A starts a project and impressively completes 75% of it in just 15 days. Realizing the deadline is approaching, they call in B to help finish the remaining 25% in 5 days. If B were to take on the entire project alone, how many days would it take them to complete it?
Check Solution
Ans: B) 25 days
A’s 1-day work = $( \frac{75\%}{15} = 5\% )$. Remaining work = 25%, done by A and B in 5 days, so (A + B)’s daily work = $( \frac{25\%}{5} = 5\% )$. B’s work rate = $( 5\% – 5\% = 3\% )$, so B alone needs $( \frac{100}{5} = 25 )$ days.
Q. 7 Three pipes—A, B, and C—are connected to a large tank. Pipes A and B can fill the tank in 20 and 30 hours, respectively, while pipe C, a drain, can empty the tank in 15 hours. Initially, pipes A and B were open for 10 hours. Then, for some reason, pipe C is opened. How much additional time will it take to fill the tank completely with all three pipes in operation?
Check Solution
Ans: B) 10 hours
Total work = ( 1 ) tank (100%). A + B’s combined rate = $( \frac{1}{20} + \frac{1}{30} = \frac{1}{12} )$. In 10 hours, $( \frac{10}{12} = \frac{5}{6} )$ of the tank is filled. Remaining work = $( \frac{1}{6} )$, with net rate $( \frac{1}{12} – \frac{1}{15} = \frac{1}{60} )$. Time = $( \frac{1}{6} \div \frac{1}{60} = 10 )$ hours.
Q. 8 Three friends, A, B, and C, take on a unique task. A is the fastest and can finish it in 15 days, B in 20 days, and C in 30 days. To speed things up, they devise a plan: A starts the work, and B and C join him alternately each day. With this dynamic schedule, how many days will it take to complete the task?
Check Solution
Ans: B) 8 days
One day of A = $( \frac{1}{15} )$, B = $( \frac{1}{20} )$, C = $( \frac{1}{30} )$. Combined work of (A + B + C) in 2 days = $( \frac{1}{15} + \frac{1}{20} + \frac{1}{30} = \frac{3}{20} )$. In 8 days (4 cycles), work done = $( \frac{12}{15} = 1 )$.
Q. 9 A and B join forces to complete a project. A can complete the job in 16 days, while B takes only 12 days. They work together seamlessly, but B has to leave 4 days before the project is completed. Despite this setback, the work is finished on time. How many days does it take in total to complete the project?
Check Solution
Ans: C) 12 days
Let total work be ( W = 48 ) units (LCM of 16 and 12). Work rate of A = 3 units/day, and B = 4 units/day. If they work together for ( x ) days, then A works alone for the last 4 days. Work done by A in last 4 days = $( 3 \times 4 = 12 )$ units, so work done together = 48 – 12 = 36. $( 7x = 36 \Rightarrow x = 8 )$. Total time = 8 + 4 = 12 days.
Q. 10 Anand Bhai is known for being twice as efficient as Balwir Paji. When Anand takes on a task alone, he can complete it in 18 days. How many days will it take if both Anand and Balwir work together, combining their efforts to finish the task?
Check Solution
Ans: C) 12 days
A’s work rate = $( \frac{1}{18} )$, and B’s work rate = $( \frac{1}{36} )$. Combined rate = $( \frac{1}{18} + \frac{1}{36} = \frac{1}{12} )$. Thus, they will finish in 12 days.
Q. 11 The plumber can fix the pipes in 10 hours. How much of the work will be done in 5 hours?
Check Solution
Ans: D
Rate of work = 1/ 10
Total work done = (1/10) * 5 * 100 %
Q. 12 A team of 25 workers can build a bridge in 36 days. How long will it take for 6 workers to finish the bridge?
Check Solution
Ans: C
Rate of work = 1/ (25*36). So, total time it will take to do the work = 25*36/6 = 150
Q. 13 Isabella can write a script in 14 days, and Charlotte can write it in 13 days. If they work together, how long will it take to finish the script?
Check Solution
Ans: A
Rate of work together will be = 1/ 14 + 1/13). So, total time it will take to do the work will be inverse of their combined rate of work = 14*13/27 = 6.7
Q. 14 Three robots have the capability to complete a task in 6 hours, 7 hours, and 8 hours respectively. What is the maximum portion of the task that two of these robots can complete together within one hour?
Check Solution
Ans: A
Rates of three robots respectively are $\frac{1}{6}$,
$\frac{1}{7}$, and $\frac{1}{8}$.
To maximize the greatest part of the work that gets done, we need the two fastest robots, i.e., those which take less time to do more work, and we need their combined rate.
$\frac{1}{6}$ + $\frac{1}{7}$ = $\frac{13}{42}$.
Greatest part of work that can be done by two fastest robots together in 1 hour?
$r*t = W$ —> $\frac{13}{42}$ * 1 = $\frac{13}{42}$.
Q. 15 At the rate of c calories per s seconds , how many calories are burned in x minutes ?
Check Solution
Ans: C
There are 60 seconds in a minute. So, in x minutes, there are $x \times 60 = 60x$ seconds.
At the rate of c calories per s seconds, the number of calories burned in x minutes is $c \times 60x = 60cx$ calories.
Q. 16 Emily has to complete typing a 1950-word paper by 5 pm. If she starts typing two hours before the deadline, her speed will be 20 words per minute. However, for every two minutes she starts after 3 pm, her typing speed will increase by one word per minute. What is the latest time Emily can start typing and still meet her deadline?
Check Solution
Ans: D
We will start by assuming the last time:
(E) 4:42 pm
If she starts typing 18 mins before the deadline, she has 18 mins to type 1950 words. Her speed at this time will be 20 + (the mins passed after 3)/2 words i.e. her speed at 4:42 will be
20 + (120 – 18)/2 = 71 words/min
She can type a total of 18 * 71 = 1278 words.
Not enough since she has to type 1950 words. She must start earlier.
(D) 4:30 pm
If she starts 30 mins before deadline, she has 30 mins to type 1950 words. Her speed at this time will be 20 + (120 – 30)/2 = 65 words/min
She can type a total of 30*65 = 1950 words
This is enough.
So she can start at 4:30
Let’s look at the algebraic solution too though backsolving is the best way way here.
Let’s say she starts her paper T mins before 5 pm.
Speed = 20 + (120 – T)/2
Time to type = T min
Words typed = 80 – T/2
We need this expression to be not less than 1950
(80 – T/2)*T = 1950
160T – T^2 = 2*1950
T^2 – 160T + 2*1950 = 0
(T – 30)(T – 130) = 0
T can be 30 or 130. The only possible option when two hrs are left is 30 mins.
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