Aptitude Questions on Time and Work
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Review Time and Work Concepts
Q. 1 A contractor has a challenging project to complete within a strict deadline of 20 days. To tackle this, they initially hire 45 workers. After 10 days of diligent labor, they discover that only 60% of the work has been finished. With time running out, the contractor needs to decide how many additional workers to bring in to ensure the project is completed on time. Please calculate the number of workers required to meet the deadline?
A) 10
B) 15
C) 20
D) 25
Check Solution
Ans: (B) 15
Total work rate for 45 workers = $( \frac{60\%}{10} = 6\% )$ per day. Remaining work = $( 40\% )$ in 10 days, so required rate = $( 4\% )$ per day. New number of workers = $( \frac{4\%}{6\%} \times 45 = 30 )$. Additional workers needed = $( 30 – 45 = 15 )$.
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 harmoniously 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?
A) 24 days
B) 20 days
C) 40 days
D) 45 days
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.
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?
A) 25
B) 20
C) 30
D) 15
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?
A) 30 days
B) 24 days
C) 15 days
D) 28 days
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 A bustling 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?
A) 60 days
B) 70 days
C) 80 days
D) 90 days
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?
A) 20 days
B) 25 days
C) 30 days
D) 35 days
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?
A) 5 hours
B) 10 hours
C) 8 hours
D) 6 hours
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?
A) 6 days
B) 8 days
C) 10 days
D) 12 days
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?
A) 8 days
B) 10 days
C) 12 days
D) 14 days
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?
A) 9 days
B) 10 days
C) 12 days
D) 15 days
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.
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