Aptitude Questions on Time and Work for Placements
Welcome to our practice page dedicated to helping you ace Time and Work questions for placement aptitude tests! This page is packed with carefully crafted questions designed to build your skills in solving a range of questions. Practice, review solutions, and keep challenging yourself. With consistent practice, you’ll develop a solid foundation to handle any Time and Work problem that comes your way!
Q. 1 A contractor hired 45 workers to complete a work in 20 days. After 10 days, only 60% of the work was done. How many more workers must be hired to complete the work on time?
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 A can do a job in 40 days, and B can do it in 30 days. They start working together, but after 10 days, C joins them and they complete the work in the next 5 days. In how many days can C alone do the work?
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 If 10 women can complete a work in 15 days, how many women are needed to complete the work in 5 days?
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 together can do a work in 12 days. A alone can do it in 20 days. In how many days can B alone do the work?
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 If 8 men and 6 women can complete a work in 10 days, and 10 men and 8 women can complete the same work in 8 days, how long will it take for 1 man and 1 woman to complete the work?
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 A does 75% of a work in 15 days. He then calls in B, and they complete the remaining work in 5 days. How long would it take for B alone to complete the entire work?
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 Two pipes A and B can fill a tank in 20 and 30 hours, respectively. Pipe C can empty the tank in 15 hours. If A and B are opened together and after 10 hours C is also opened, how much more time will it take to fill the tank?
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 people, A, B, and C, can complete a work in 15, 20, and 30 days, respectively. If A starts working and B and C join him every alternate day, in how many days will the work be finished?
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 can do a piece of work in 16 days, and B can do it in 12 days. They start working together, but B leaves 4 days before the work is completed. How long does the total work take?
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 If A is twice as efficient as B and can complete a job in 18 days, how many days will it take for both A and B working together to finish the job?
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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