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

There are twenty people working in an office. The first group of five works between 8:00 a.m. and 2:00 p.m. The second group of ten works between 10:00 a.m. and 4:00 p.m. The third group of five works between 12 noon and 6:00 p.m. There are three computers in the office which all the employees frequently use. During which of the following hours are the computers likely to be used the most?

  1. 10:00 a.m. – 12 noon

  2. 12 noon – 2:00 p.m.

  3. 1:00 p.m. – 3:00 p.m.

  4. 2:00 p.m. – 4:00 p.m.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Clearly, the computers would be used the most when all the three groups are working simultaneously and this happens during the period of 12 noon to 2:00 p.m.

Multiple choice

A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 8.00 a.m., at what time will he first touch a flag at 120 feet from the ground?

  1. 4 p.m.

  2. 5 p.m.

  3. 6 p.m.

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The monkey climbs 30 feet and slips back 20 feet each hour, gaining 10 feet net per hour. After 7 hours (from 8 a.m. to 3 p.m.), he reaches 70 feet. At the beginning of the 8th hour (starts at 3 p.m.), he climbs 30 feet from 70 to 100 feet. At the beginning of the 9th hour (starts at 4 p.m.), he climbs from 100 to 130 feet, touching the 120-foot flag at 6 p.m. (after 10 hours from 8 a.m., which is 6 p.m.).

Multiple choice

A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing in the beginning of the next hour. If he begins his ascent at 8.00 a.m. at what time will he touch a flag which is 120 feet from the ground?

  1. 4 p.m.

  2. 5 p.m.

  3. 6 p.m.

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Net climb per hour = 30 - 20 = 10 ft. After 9 hours (8am to 5pm), monkey reaches 90 ft. At 5pm, starts at 90 ft, climbs 30 ft to reach 120 ft exactly. No slip back occurs because goal is reached during the climb.

Multiple choice

Suman takes thrice as much time as Rahul and four times as much as Varun to finish a task. They together complete the task in one day. Find the time taken by each of them to complete the task.

  1. 6 days

  2. 14 days

  3. 5 days

  4. 10 days

  5. 8 days
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

It is correct answer.

Let alone time of Suman be x .

Then alone time of Rahul = x/3 and that of Varun be x/4.

Suman's one day work + Rahul's one day work + Varun's one day work = Combined one day work                     

   (1/x) + (1/(x/3)) + (1/(x/4)) = 1                                                  x = 8

Multiple choice

A and B can do a piece of work in 6 days. B and C can do it in 7½ days. C and A can do it in 10 days. In how many days will B alone finish it?

  1. 30 days

  2. 10 days

  3. 15 days

  4. 1/10 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

( A + B ) 's  1 day work  = 1 / 6( B + C ) 's 1 day work = 2 / 15       ( 7 1/2 = 15 /2 ) ( C + A )'s 1 day work = 1/ 10By adding

( A+ B ) + ( B + C ) + ( C + A ) 's 1 day work = 1/ 6 + 2/15 + 1/10  (A + B + B + C + C + A) 's 1 day work = 1/ 6 + 2/15 + 1/10  ( 2A + 2B + 2C ) 's 1 day work = 1/6 + 2/15 + 1/10 2 ( A + B + C ) 's 1 day work = (5 + 4 + 3) /30 = 12/30 = 6 /15 (A + B + C )'s 1 day work = 6/15 x 2 = 6/30

( A + B + C ) 's 1 day work - ( C + A ) 's 1 day work =                                  6/30 - 1/10                                 = 6 - 3 /30                                = 3/30                                  = 1 /10 B1 day work is 1/10 B can complete whole work in  1 / 1/10 = 10 days

Multiple choice

The work done by A in one day is half of the work done by B in one day. The work done by B is half of the work done by C in one day. If C alone can complete the work in 7 days, in how many days will A, B and C together complete the work?

  1. 28 days

  2. 14 days

  3. 4 days

  4. 21 days

  5. 8 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work done by C in one day = 1/7 Work done by B in one day = 1/2(C) = 1/7 x 1/2 = 1/14 Work done by A in one day = 1/2(B) = 1/2 x 1/14 = 1/28 Work done by A, B and C together in one day = (4 + 2 + 1)/28 = 1/4 Work is done by A, B and C together in 4 days.

Multiple choice

A can do a piece of work in 10 days and B can do the same work in 14 days. How long will they take if both of them work together?

  1. 35/6 days

  2. 6/35 days

  3. 6 days

  4. 60/11 days

  5. 12 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's 1 day's work = 1/10th part of the whole work and  B's 1 day's work = 1/14th part of the whole work. Therefore, (A + B)'s one day's work = 1/10 + 1/14 = 6/35th part of the whole work. So, both will complete the work in 35/6 days. It is the correct answer.

Multiple choice

A piece of work can be finished by 12 men in 12 days, whereas it takes 16 women 12 days to finish the same work. If 18 men and 8 women undertake the responsibility to complete the work, how many days will it take them to complete it?

  1. 7 days

  2. 6 days

  3. 24 days

  4. 5 days

  5. 8 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 It is clear that 12 men = 16 women or 3 men = 4 women.  Therefore, 18 men + 8 women =18 * (4 / 3) women + 8 women  = 24 + 8 = 32 women 
Now, 16 women can complete the work in 12 days. So, 32 women will do it in 6 days. ((12 * 16) / 32 = 6 days).  It is the correct answer.

Multiple choice

A can do a work in 4 days. B completes the same work in 8 days. C takes as long as A and B would take if they worked together. How long will it take B and C to complete the work if they work together?

  1. 3 days

  2. 12/5 days

  3. 32/3 days

  4. 8/3 days

  5. 2 days
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

(A + B) can do the work in (4 * 8) / (4 + 8) = 32/12 = 8/3 days

Therefore, C takes 8/3 days to complete the work. So, (B + C) takes ((8/3) * 8)/((8/3) + 8) = 64/32 = 2 days. It is the correct answer.

Multiple choice

A can do a piece of work in 18 days and B can do the same work in 24 days. They finished the work with the assistance of C in 6 days and got Rs. 51 as their wage. Find the share of B in the wage?

  1. Rs. 11.25

  2. Rs. 17

  3. Rs. 12.75

  4. Rs. 11.75

  5. Rs. 21.25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A did 1/3th of the workin 6 days. B completed 1/4th of the work in 6 days. Work completed by C in 6 days = 1 - (1/3) + (1/4) = 5/12th of the work Since A, B and C did the work in 6 days 1/3th, 1/4th, 5/12th of the work, respectively. A's share = Rs 51 * (1 / 3) = Rs. 17 B's share = Rs 51 * (1 / 4) = Rs. 12.75 C's share = Rs 51 * (5 / 12) = Rs. 21.25. So B's share is Rs 12.75. It is the correct answer.