Time And Work MCQs

A contractor estimates that he can complete a project in 12 days if he works full days. However, due to heat restrictions, he can work only 75% of each day. How many days will he actually take to complete the project?

14 days
15 days
16 days
18 days

Explanation: If the full-day efficiency is 1/12 of the project per day, working at 75% capacity means the daily output becomes (1/12) × (3/4) = 1/16 of the project. Therefore, the total time required is the reciprocal: 1 ÷ (1/16) = 16 days.

A skilled artisan can finish an order in 10 days. After working for 4 days, his tools get damaged and his efficiency falls by 25%. How many days in total does he take to complete the order?

11 days
12 days
13 days
14 days

Explanation: In the first 4 days, the artisan completes 4/10 = 2/5 of the order. The remaining 3/5 must be completed at reduced efficiency. A 25% drop means he now works at 75% of his original rate, so his new daily output is (1/10) × (3/4) = 3/40. The time needed for the remainder is (3/5) ÷ (3/40) = 8 days. Adding the initial 4 days gives a total of 12 days.

A weaver can complete a tapestry in 18 days. After working for 6 days, he acquires a better loom that increases his efficiency by 50%. How many days does he take to complete the entire tapestry?

12 days
13 days
14 days
15 days

Explanation: In 6 days, the weaver completes 6/18 = 1/3 of the tapestry. The remaining 2/3 is woven at the improved rate. A 50% increase in efficiency means the new daily output is (1/18) × (3/2) = 1/12 of the tapestry. The time to finish the remainder is (2/3) ÷ (1/12) = 8 days. The total time is 6 + 8 = 14 days.

A project manager works on a report at a rate of 1/6 per day on Mondays and Tuesdays, and at a rate of 1/12 per day from Wednesday to Friday. He does not work on weekends. How many days does he take to complete the report?

6 days
7 days
8 days
9 days

Explanation: Each five-day week, the manager completes 2 × (1/6) + 3 × (1/12) = 1/3 + 1/4 = 7/12 of the report. After the first week (5 days), 7/12 is done and 5/12 remains. In the next week, Monday adds 1/6 = 2/12 (total 9/12), Tuesday adds another 2/12 (total 11/12), and Wednesday adds 1/12 to finish the report. Counting the days gives 5 + 3 = 8 days.

A craftsman takes 10 days to produce the first unit of an artifact. With each subsequent unit, his time reduces by exactly 1 day due to practice. How many days does he take to produce the first 3 units?

24 days
25 days
27 days
30 days

Explanation: The time for the first unit is 10 days, the second unit takes 9 days, and the third unit takes 8 days. The total time is the sum of this arithmetic sequence: 10 + 9 + 8 = 27 days.

Technician X is three times as efficient as technician Y. X completes the same assignment 12 days earlier than Y. How many days does Y take to complete the assignment alone?

15 days
16 days
18 days
20 days

Explanation: If X is three times as efficient, he takes one-third of the time that Y takes. Let Y's time be T days; then X takes T/3 days. The difference is T − T/3 = 2T/3, which equals 12 days. Solving 2T/3 = 12 gives T = 18 days.

Engineer P is 50% more efficient than engineer Q. Working together, they can complete a design in 18 days. How many days would Q alone take to complete the same design?

36 days
40 days
45 days
50 days

Explanation: A 50% efficiency advantage means P's daily output is 1.5 times Q's daily output. If Q alone takes T days, P alone takes T/1.5 days. Their combined daily work is 1/T + 1.5/T = 2.5/T. Setting this equal to 1/18 gives 2.5/T = 1/18, so T = 2.5 × 18 = 45 days.

In a factory, machine A produces 16 units per hour and machine B produces 8 units per hour. How many days will they take to jointly produce 384 units if both operate 8 hours per day?

1 day
2 days
3 days
4 days

Explanation: The combined hourly output is 16 + 8 = 24 units. To produce 384 units, they need 384 ÷ 24 = 16 hours of operation. At 8 hours per day, this translates to 16 ÷ 8 = 2 days.

Three masons can build a wall individually in 10, 15, and 30 days respectively. All three start together, but after 2 days the fastest mason leaves. How many days in total are needed to complete the wall?

6 days
7 days
8 days
9 days

Explanation: The combined daily output of all three is 1/10 + 1/15 + 1/30 = 1/5 of the wall. In 2 days they complete 2/5 of the wall, leaving 3/5. The remaining two masons together build 1/15 + 1/30 = 1/10 per day. To finish 3/5 at this rate requires (3/5) ÷ (1/10) = 6 days. The total duration is 2 + 6 = 8 days.

Pairwise, teams of workers can finish a task as follows: the first pair in 12 days, the second pair in 15 days, and the third pair in 20 days. If all three workers now collaborate together, how many days will they take?

8 days
9 days
10 days
12 days

Explanation: Adding the three pairwise rates gives twice the combined rate of all three workers: 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5. Half of this sum, 1/10, is the daily output of all three together. Hence, the time required is 1 ÷ (1/10) = 10 days.

A painter can complete a mural in 20 days, while his assistant would take 30 days. The painter works alone for 5 days, and then the assistant joins him. How many more days are needed to finish the mural?

7 days
8 days
9 days
10 days

Explanation: In 5 days, the painter completes 5/20 = 1/4 of the mural, leaving 3/4. When both work together, their daily output is 1/20 + 1/30 = 1/12. The remaining 3/4 is therefore completed in (3/4) ÷ (1/12) = 9 days.

Two workers can individually complete a task in 12 days and 18 days. They begin together, and after 6 days a third worker—who alone takes 36 days—joins them. How many days in total are needed to finish the task?

5 days
6 days
7 days
8 days

Explanation: The first two workers together complete 1/12 + 1/18 = 5/36 of the task per day. In 6 days they finish 6 × (5/36) = 5/6 of the task, leaving 1/6. With the third worker, the trio completes 1/12 + 1/18 + 1/36 = 1/6 per day. The remaining 1/6 therefore requires exactly 1 more day, giving a total of 7 days.

Three labourers have efficiencies in the ratio 3 : 2 : 1. Working together, they finish a construction job in 12 days. How many days would the second labourer take to complete the same job working alone?

24 days
30 days
36 days
48 days

Explanation: Let the daily outputs be 3x, 2x, and x. Their combined daily output is 6x, which equals 1/12 of the job. Solving 6x = 1/12 gives x = 1/72. The second labourer's daily output is 2x = 2/72 = 1/36. Therefore, he alone needs 1 ÷ (1/36) = 36 days.

Two teams can finish a survey as follows: the senior team and the junior team together take 20 days, while the junior team and the trainee take 24 days. The senior team is three times as efficient as the junior team. How many days would the senior team and the trainee take together?

12 days
14 days
15 days
16 days

Explanation: Let the junior team's daily output be x. Then the senior team's output is 3x. From the first pair, 3x + x = 1/20, so x = 1/80. The senior rate is 3/80. From the second pair, the trainee's rate is 1/24 − 1/80 = 7/240. Adding the senior and trainee rates gives 3/80 + 7/240 = 16/240 = 1/15. Hence, the senior–trainee pair needs 15 days.

Three analysts can individually complete a market study in 15 days, 24 days, and 40 days respectively. When all four analysts (including a new recruit) work together, the study is finished in 6 days. How many days would the new recruit take to complete the study alone?

25 days
28 days
30 days
32 days

Explanation: The three existing analysts together complete 1/15 + 1/24 + 1/40 = 8/120 + 5/120 + 3/120 = 16/120 = 2/15 of the study per day. All four together complete 1/6 per day. Therefore, the recruit's daily contribution is 1/6 − 2/15 = 5/30 − 4/30 = 1/30. Working alone, the recruit would need 30 days.

Two carpenters can build a cabinet in 6 days and 12 days respectively. They work on alternate days, starting with the faster carpenter. How many days are needed to complete the cabinet?

6 days
7 days
8 days
9 days

Explanation: Every two-day cycle, the work completed is 1/6 + 1/12 = 1/4 of the cabinet. After three full cycles (6 days), 3/4 is finished and 1/4 remains. On the 7th day, the faster carpenter completes 1/6, leaving 1/4 − 1/6 = 1/12. On the 8th day, the slower carpenter finishes exactly 1/12. The total time is 8 days.

Three electricians can wire a building individually in 6 days, 9 days, and 18 days. They work in a repeating rotation: first electrician one day, second the next, third the next, and so on. How many days does the entire wiring take?

7 days
8 days
9 days
10 days

Explanation: Each three-day rotation completes 1/6 + 1/9 + 1/18 = 6/18 = 1/3 of the wiring. After two full rotations (6 days), 2/3 is done and 1/3 remains. On the 7th day, the first electrician completes 1/6, leaving 1/6. On the 8th day, the second electrician completes 1/9, leaving 1/18. On the 9th day, the third electrician finishes exactly 1/18. The total is 9 days.

Three programmers can complete a module individually in 12, 18, and 36 days. All three start together, but after 2 days the middle programmer takes a 3-day break while the other two continue. She then rejoins. How many days in total are needed to complete the module?

5 days
6 days
7 days
8 days

Explanation: All three together complete 1/12 + 1/18 + 1/36 = 1/6 of the module per day. In 2 days they finish 1/3, leaving 2/3. While the middle programmer is away, the other two complete 1/12 + 1/36 = 1/9 per day; in 3 days they finish another 1/3, leaving 1/3. With all three back together at 1/6 per day, the remaining 1/3 takes (1/3) ÷ (1/6) = 2 days. The total is 2 + 3 + 2 = 7 days.

An overhead tank can be filled by two inlet pipes in 12 hours and 18 hours respectively. A third pipe acts as an outlet and can empty the full tank in 36 hours. If all three pipes are opened simultaneously when the tank is empty, how many hours will it take to fill the tank?

6 hours
8 hours
9 hours
10 hours

Explanation: The net inflow per hour is the sum of the inlet rates minus the outlet rate: 1/12 + 1/18 − 1/36 = 3/36 + 2/36 − 1/36 = 4/36 = 1/9 of the tank. Therefore, the tank fills in 1 ÷ (1/9) = 9 hours.

A pump can fill a reservoir in 12 hours at full capacity. Because of a partial clog, it runs at only 75% efficiency for the first 4 hours, after which the clog clears. How many hours in total does it take to fill the reservoir?

11 hours
12 hours
13 hours
14 hours

Explanation: At 75% efficiency, the pump's rate is (1/12) × (3/4) = 1/16 per hour. In 4 hours it fills 4 × (1/16) = 1/4 of the reservoir. The remaining 3/4 is filled at the full rate of 1/12 per hour, requiring (3/4) ÷ (1/12) = 9 hours. The total time is 4 + 9 = 13 hours.

A pipe can fill a cistern in 10 hours. Because of a leak at the bottom, it now takes 15 hours to fill the cistern. How many hours would the leak take to empty a full cistern?

20 hours
25 hours
30 hours
35 hours

Explanation: The pipe's filling rate is 1/10 of the cistern per hour. With the leak, the effective rate drops to 1/15. The difference, 1/10 − 1/15 = 1/30, is the leak's emptying rate. Consequently, a full cistern would be emptied by the leak in 30 hours.

Two inlet pipes can fill a tank in 8 hours and 16 hours. After running together for 2 hours, a leak develops that can empty the full tank in 16 hours. How many hours in total are needed to fill the tank?

5 hours
6 hours
7 hours
8 hours

Explanation: In the first 2 hours, the two pipes together fill 2 × (1/8 + 1/16) = 2 × (3/16) = 3/8 of the tank. The remaining 5/8 is filled while the leak is active. The net rate then becomes 1/8 + 1/16 − 1/16 = 1/8 per hour. The remaining 5/8 therefore requires (5/8) ÷ (1/8) = 5 hours. The total time is 2 + 5 = 7 hours.

Two supply pipes can fill a water tank in 12 hours and 18 hours. They are opened together for 4 hours, after which a drain pipe that can empty the full tank in 36 hours is also opened. How many hours in total does it take to fill the tank?

6 hours
7 hours
8 hours
9 hours

Explanation: In 4 hours, the two supply pipes fill 4 × (1/12 + 1/18) = 4 × (5/36) = 5/9 of the tank. The remaining 4/9 is filled with the drain open. The net filling rate then becomes 1/12 + 1/18 − 1/36 = 4/36 = 1/9 per hour. The remaining 4/9 therefore requires (4/9) ÷ (1/9) = 4 hours. The total time is 4 + 4 = 8 hours.

A booster pump can fill a storage tank in 10 hours. It runs at full capacity for the first 3 hours, then at 50% capacity for the next 4 hours due to power throttling, and finally returns to full capacity. How many hours in total does it take to fill the tank?

10 hours
11 hours
12 hours
13 hours

Explanation: At full capacity, the pump fills 3/10 of the tank in the first 3 hours. At 50% capacity, its rate is 1/20 per hour, so in 4 hours it fills 4/20 = 1/5. The combined progress after 7 hours is 3/10 + 1/5 = 1/2. The remaining half is filled at the full rate of 1/10 per hour, requiring 5 more hours. The total is 3 + 4 + 5 = 12 hours.

A sump has two inlet pumps that can fill it in 6 hours and 9 hours, and one outlet pump that can empty it in 18 hours. If all three pumps are started when the sump is empty, how many hours will it take for the sump to be two-thirds full?

2 hours
3 hours
4 hours
5 hours

Explanation: The net filling rate is 1/6 + 1/9 − 1/18 = 3/18 + 2/18 − 1/18 = 4/18 = 2/9 of the sump per hour. To reach two-thirds capacity, the time required is (2/3) ÷ (2/9) = 3 hours.

An inlet pipe can fill a tank in 9 hours. A leak at the bottom can empty the full tank in 18 hours, but it only starts operating once the tank is one-third full. How many hours does it take to fill the tank completely?

12 hours
13 hours
14 hours
15 hours

Explanation: The first one-third is filled by the inlet pipe alone at 1/9 per hour, requiring (1/3) ÷ (1/9) = 3 hours. Once the leak activates, the net rate becomes 1/9 − 1/18 = 1/18 per hour. The remaining two-thirds therefore needs (2/3) ÷ (1/18) = 12 hours. The total time is 3 + 12 = 15 hours.

Three workers with efficiencies in the ratio 3 : 2 : 1 complete a contract. The total payment for the job is ₹1800. If the wage is distributed in proportion to their efficiencies, how much does the second worker receive?

₹400
₹500
₹600
₹700

Explanation: The second worker's share is determined by the ratio of his efficiency to the total efficiency. The total parts are 3 + 2 + 1 = 6. The second worker gets 2/6 of ₹1800, which equals ₹600.

Two workers can complete a job in 10 days and 15 days. They agree to a total wage of ₹2250 distributed according to work done. They start together, but the second worker leaves after 5 days while the first worker completes the rest. What is the first worker's share?

₹1250
₹1400
₹1500
₹1600

Explanation: Together they complete 5 × (1/10 + 1/15) = 5/6 of the job in 5 days. The remaining 1/6 is done by the first worker alone at 1/10 per day, taking (1/6) ÷ (1/10) = 5/3 days. The first worker's total contribution is (5 + 5/3) × (1/10) = 2/3 of the job. His wage is therefore (2/3) × ₹2250 = ₹1500.

Worker X is twice as efficient as worker Y. Together they finish a project in 12 days for a total fee of ₹3600, with payment proportional to work done. What is the difference between their individual earnings?

₹800
₹1000
₹1200
₹1500

Explanation: If Y's daily output is x, then X's is 2x. Their combined output is 3x = 1/12, so x = 1/36. X's rate is 2/36 = 1/18 and Y's is 1/36. X therefore does (1/18) ÷ (1/12) = 2/3 of the work, earning (2/3) × ₹3600 = ₹2400. Y earns the remaining ₹1200. The difference is ₹1200.

Three craftsmen can complete an order in 8, 12, and 16 days respectively. The total contract value is ₹4400, to be shared in proportion to work done. All three work for 2 days, after which the third craftsman leaves and the other two complete the job. What is the third craftsman's payment?

₹450
₹500
₹550
₹600

Explanation: The third craftsman works only the initial 2 days at a rate of 1/16 per day, contributing 2/16 = 1/8 of the total work. Since payment is proportional to work done, his share is (1/8) × ₹4400 = ₹550.

Two contractors can complete a renovation in 15 days working together; the senior contractor alone would take 20 days. The total budget is ₹3000, split according to work done. They work together for 6 days, then the senior contractor leaves and the junior one finishes the job. What is the junior contractor's total payment?

₹1800
₹1900
₹2100
₹2200

Explanation: The junior contractor's daily rate is 1/15 − 1/20 = 1/60. In the first 6 days, both together complete 6/15 = 2/5 of the job. The remaining 3/5 is done by the junior contractor alone at 1/60 per day, requiring 36 days. His total work share is (6 + 36) × (1/60) = 7/10. His payment is therefore (7/10) × ₹3000 = ₹2100.

Three artisans can complete a commission individually in 12, 18, and 36 days. The total fee of ₹3600 is divided according to work done. All three start together, but the third artisan leaves after 3 days and the second artisan leaves after 6 days; the first artisan completes the job alone. What is the first artisan's share?

₹1800
₹1900
₹2100
₹2400

Explanation: All three together complete 1/12 + 1/18 + 1/36 = 1/6 per day. In the first 3 days, half the commission is finished. The remaining two artisans then work at 1/12 + 1/18 = 5/36 per day; in the next 3 days they complete another 5/12, leaving 1/12. The first artisan finishes this remainder alone in 1 day at 1/12 per day. His total contribution is 7/12 of the work, so his share is (7/12) × ₹3600 = ₹2100.

Four men and two boys can complete a project in 8 days, while two men and four boys can complete the same project in 12 days. If payment is always proportional to work done, how many times more does a man earn than a boy for the same amount of work?

2 times
3 times
4 times
5 times

Explanation: Let a man's daily output be m and a boy's be b. From the two groups, 4m + 2b = 1/8 and 2m + 4b = 1/12. Doubling the first equation and subtracting the second gives 6m = 1/4 − 1/12 = 1/6, so m = 1/36. Substituting back yields b = 1/144. The ratio of their outputs is (1/36) : (1/144) = 4 : 1. Since payment is proportional to work, a man earns 4 times what a boy earns.

Two engineers can complete a design in 10 days and 15 days respectively. They are paid ₹3000 proportionally to work done. They work together for 4 days, after which the second engineer leaves and the first engineer completes the design alone. How much does the second engineer earn?

₹600
₹700
₹800
₹900

Explanation: Together they complete 4 × (1/10 + 1/15) = 4 × (1/6) = 2/3 of the design in 4 days. The second engineer contributes only during these 4 days at 1/15 per day, so his total work share is 4/15. His payment is therefore (4/15) × ₹3000 = ₹800.

A clerk can process a full batch of files in 12 days if he works continuously. However, he follows a schedule of working 3 days and then taking 1 day off. How many calendar days does he take to finish the entire batch?

12 days
13 days
14 days
15 days

Explanation: Every 4-day cycle, the clerk works 3 days and completes 3/12 = 1/4 of the batch. After three such cycles (12 calendar days), 9/12 = 3/4 is done. The remaining 1/4 requires 3 more work days. These are days 13, 14, and 15, with no further break needed because the job is finished. The total is 15 calendar days.

Two technicians can service a network individually in 6 days and 12 days. The first technician works 2 days and rests 1 day; the second works 3 days and rests 1 day. They start together. How many days does it take to complete the servicing?

4 days
5 days
6 days
7 days

Explanation: On day 1, both work and complete 1/6 + 1/12 = 1/4. On day 2, both work again and the total reaches 1/2. On day 3, only the second technician works, adding 1/12 to reach 7/12. On day 4, only the first technician works, adding 1/6 to reach 3/4. On day 5, both are back on duty and add another 1/4, completing the job. The total is 5 days.

A surveyor can complete a mapping project in 30 days if he works every day. However, his contract requires him to work 5 consecutive days and then take 2 days off. How many calendar days does he take to finish the project?

35 days
37 days
40 days
42 days

Explanation: Each 7-day week, the surveyor works 5 days and completes 5/30 = 1/6 of the project. After five full weeks (35 calendar days), 25/30 = 5/6 is finished. The remaining 1/6 requires 5 more work days, which are days 36 through 40. The project is therefore completed on the 40th calendar day.

Two researchers can complete a study in 12 days and 18 days respectively. The first researcher works alone for 4 days, then falls ill for 2 days during which the second researcher continues alone. They then work together to finish. How many days in total does the study take?

8 days
9 days
10 days
11 days

Explanation: The first researcher completes 4/12 = 1/3 in 4 days. While he is ill, the second researcher completes 2/18 = 1/9 in 2 days. The remaining work is 1 − 1/3 − 1/9 = 5/9. Working together, their combined rate is 1/12 + 1/18 = 5/36. The remaining 5/9 therefore requires (5/9) ÷ (5/36) = 4 days. The total duration is 4 + 2 + 4 = 10 days.

A technician can complete a calibration in 14 days by working 8 hours each day without breaks. If he introduces a mandatory 1-hour lunch break every working day, how many days will the calibration now take?

14 days
15 days
16 days
17 days

Explanation: The total calibration work is 14 × 8 = 112 technician-hours. With a 1-hour lunch break, each day contributes only 7 effective hours. The number of days required is therefore 112 ÷ 7 = 16 days.

A machinist can finish a production run in 10 days by working 6 hours each day. Due to a power shortage, he works only 4 hours per day for the middle 3 days of the project, while maintaining 6 hours per day on all other days. How many days does he take to complete the run?

9 days
10 days
11 days
12 days

Explanation: The total work is 10 × 6 = 60 machinist-hours. In the first 4 days, he completes 4 × 6 = 24 hours. During the 3-day shortage, he completes 3 × 4 = 12 hours. The remaining work is 60 − 24 − 12 = 24 hours, which he finishes at 6 hours per day in 4 more days. The total duration is 4 + 3 + 4 = 11 days.

Two farmers can plough a field individually in 8 days and 16 days. The first farmer works 3 days and rests 1 day, repeating this pattern. The second farmer works continuously. How many days do they take to plough the field together?

5 days
6 days
7 days
8 days

Explanation: On each day both work, they complete 1/8 + 1/16 = 3/16 of the field. In the first 3 days, they finish 9/16. On day 4, only the second farmer works, adding 1/16 to reach 10/16 = 5/8. On days 5 and 6, both work again and add another 6/16, completing the field. The total is 6 days.

A welder can complete a structural joint in 6 days by working 6 hours on the first day. To meet a deadline, he increases his daily working time by 2 hours each successive day. On which day does he finish the job?

Day 3
Day 4
Day 5
Day 6

Explanation: The total welding work is 6 × 6 = 36 hours. The daily hours form an arithmetic sequence: 6, 8, 10, 12, ... The cumulative hours after 4 days are 6 + 8 + 10 + 12 = 36, which exactly matches the total requirement. The job is therefore completed on the 4th day.

Two men and three boys can complete a harvest in 20 days, while three men and two boys can complete the same harvest in 15 days. How many days would one man take to complete the harvest alone?

40 days
45 days
50 days
60 days

Explanation: Let a man's daily output be m and a boy's be b. The two conditions give 2m + 3b = 1/20 and 3m + 2b = 1/15. Tripling the first equation and doubling the second yields 6m + 9b = 3/20 and 6m + 4b = 2/15 = 8/60. Subtracting gives 5b = 3/20 − 2/15 = 9/60 − 8/60 = 1/60, so b = 1/300. Substituting back, 2m + 3/300 = 1/20, giving m = 1/50. One man therefore needs 50 days.

A senior analyst is 50% more efficient than a junior analyst. For the same report, the senior analyst finishes 8 days earlier than the junior analyst. How many days does the junior analyst take?

20 days
22 days
24 days
26 days

Explanation: A 50% efficiency advantage means the senior analyst takes 2/3 of the time the junior analyst takes. If the junior analyst takes T days, the senior takes 2T/3 days. The difference T − 2T/3 = T/3 equals 8 days. Solving T/3 = 8 gives T = 24 days.

Two programmers have efficiencies in the ratio 3 : 2. Working together, they can deliver a software module in 15 days. How many days would the more efficient programmer take alone?

20 days
22 days
25 days
30 days

Explanation: Let the daily outputs be 3x and 2x. Their combined output is 5x = 1/15, so x = 1/75. The more efficient programmer's rate is 3x = 3/75 = 1/25. Working alone, he therefore needs 25 days.

Three consultants have efficiencies in the ratio 2 : 3 : 5. Together, they can prepare a business plan in 12 days. How many days would the two less efficient consultants take to prepare the same plan?

18 days
20 days
24 days
30 days

Explanation: Let the daily outputs be 2x, 3x, and 5x. The combined output is 10x = 1/12, so x = 1/120. The two less efficient consultants together produce 2x + 3x = 5x = 5/120 = 1/24 of the plan per day. Hence, they need 24 days.

One man, two women, and three children are all equivalent in work capacity (i.e., 1 man = 2 women = 3 children). One man, one woman, and one child together can finish a task in 12 days. How many days would one man and two women take for the same task?

8 days
9 days
11 days
12 days

Explanation: Let a child's daily output be c. Then a woman's is 3c/2 and a man's is 3c. The mixed trio completes 3c + 3c/2 + c = 11c/2 per day, which equals 1/12. Solving gives c = 1/66. One man and two women produce 3c + 2(3c/2) = 6c = 6/66 = 1/11 per day. Therefore, they need 11 days.

Three labourers are such that the first is twice as efficient as the second, and the second is twice as efficient as the third. Together they complete a digging job in 8 days for ₹2800, paid proportionally to work done. What is the first labourer's share?

₹1200
₹1400
₹1600
₹1800

Explanation: The efficiencies are in the ratio 4 : 2 : 1. Let the daily outputs be 4x, 2x, and x. Their combined output is 7x = 1/8, so x = 1/56. The first labourer's rate is 4/56 = 1/14. His share of the total work is (1/14) ÷ (1/8) = 4/7. His wage is therefore (4/7) × ₹2800 = ₹1600.

Two architects can design a building together in 10 days. When a third architect joins them, the trio completes the same design in 6 days. How many days would the third architect take to design the building alone?

12 days
14 days
15 days
18 days

Explanation: The pair's daily output is 1/10. The trio's daily output is 1/6. The third architect's contribution is the difference: 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15. Working alone, the third architect would therefore need 15 days.

A worker pairs up with a junior colleague to complete a documentation project in 20 days. When the same worker pairs up with a senior colleague who is three times as efficient as the junior colleague, they complete the project in 12 days. How many days would the junior colleague take alone?

40 days
50 days
60 days
72 days

Explanation: Let the junior colleague's daily output be x, making the senior colleague's output 3x. If the shared worker's output is w, then w + x = 1/20 and w + 3x = 1/12. Subtracting the first equation from the second gives 2x = 1/12 − 1/20 = 5/60 − 3/60 = 2/60 = 1/30. Thus, x = 1/60. The junior colleague alone therefore needs 60 days.

Three construction crews can individually build a bridge section in 9, 12, and 18 months. In the first phase, the fastest and middle crews work together for 2 months. In the second phase, the middle and slowest crews work together for 2 months. In the final phase, the fastest and slowest crews reunite to finish the remainder. How many months in total are needed?

4 months
5 months
6 months
7 months

Explanation: Phase 1 completes 2 × (1/9 + 1/12) = 7/18 of the section. Phase 2 completes 2 × (1/12 + 1/18) = 5/18. Together, 12/18 = 2/3 is finished, leaving 1/3. The final pair works at 1/9 + 1/18 = 1/6 per month. The remaining 1/3 therefore requires (1/3) ÷ (1/6) = 2 months. The total is 2 + 2 + 2 = 6 months.

Three painters can individually complete a hall in 10, 15, and 30 days. All three start together and work for 2 days. The fastest painter then leaves, and the other two continue for 3 more days. The middle painter then also leaves, and the slowest painter finishes alone. How many days in total does the job take?

12 days
13 days
14 days
15 days

Explanation: In the first 2 days, all three complete 2 × (1/10 + 1/15 + 1/30) = 2/5 of the hall. In the next 3 days, the remaining two complete 3 × (1/15 + 1/30) = 3/10. The cumulative progress is 2/5 + 3/10 = 7/10, leaving 3/10. The slowest painter completes this remainder at 1/30 per day, requiring (3/10) ÷ (1/30) = 9 days. The total is 2 + 3 + 9 = 14 days.

Two teams can renovate a wing in 12 days and 24 days respectively. They start together, but after 4 days the first team is reassigned and a replacement team that alone would take 8 days joins the second team. How many days in total does the renovation take?

6 days
7 days
8 days
9 days

Explanation: In 4 days, the original pair completes 4 × (1/12 + 1/24) = 4 × (3/24) = 1/2 of the renovation. The remaining half is done by the second team and the replacement at 1/24 + 1/8 = 4/24 = 1/6 per day. This requires (1/2) ÷ (1/6) = 3 days. The total duration is 4 + 3 = 7 days.

Two shifts of workers can complete a factory setup in 12 days and 18 days at normal pace. They work together at normal pace for 2 days, then switch to double pace (twice the daily output) for 2 days, after which the faster team continues alone at normal pace to finish. How many days in total does the setup take?

5 days
6 days
7 days
8 days

Explanation: At normal pace, their combined daily output is 1/12 + 1/18 = 5/36. In 2 normal days they complete 10/36 = 5/18. At double pace, their combined output is 10/36 = 5/18 per day; in 2 double days they complete another 10/18 = 5/9. The cumulative progress is 5/18 + 5/9 = 15/18 = 5/6, leaving 1/6. The faster team alone at normal pace completes 1/12 per day, so the remaining 1/6 takes (1/6) ÷ (1/12) = 2 days. The total is 2 + 2 + 2 = 6 days.

Two engineers can complete a foundation in 20 days and 30 days respectively. They work together for 5 days, after which the client expands the scope to 1.5 times the original foundation. The engineers continue working together on the expanded scope. How many days in total does the entire project take?

15 days
16 days
17 days
18 days

Explanation: Their combined daily output is 1/20 + 1/30 = 1/12 of the original foundation. In 5 days they complete 5/12. The expanded scope is 3/2, so the remaining work is 3/2 − 5/12 = 13/12. At their combined rate of 1/12 per day, this remaining work requires 13 more days. The total duration is 5 + 13 = 18 days.

Three teams can individually build a road section in 15, 10, and 6 days. The slowest team works alone for 5 days. The middle team then joins for 2 days. Finally, the fastest team also joins and all three work together to finish. How many days in total does the project take?

6 days
7 days
8 days
9 days

Explanation: The slowest team completes 5/15 = 1/3 in 5 days. When the middle team joins, their combined rate is 1/15 + 1/10 = 1/6 per day; in 2 days they finish another 1/3. The cumulative progress is 2/3, leaving 1/3. With all three teams at 1/15 + 1/10 + 1/6 = 1/3 per day, the remaining 1/3 takes exactly 1 day. The total is 5 + 2 + 1 = 8 days.

A contractor commits to finishing a project in 20 days using 30 labourers, each capable of completing 1/600 of the project per day. After 10 days, 10 labourers quit. The contract imposes a penalty of ₹50 for each day of delay. What is the total penalty the contractor must pay?

₹200
₹250
₹300
₹350

Explanation: The total project size is 30 × 20 × (1/600) = 1. In 10 days, the 30 labourers complete 10 × 30 × (1/600) = 1/2 of the project. The remaining 20 labourers work at 20/600 = 1/30 per day, so they need (1/2) ÷ (1/30) = 15 days. The project therefore takes 25 days, causing a 5-day delay. The penalty is 5 × ₹50 = ₹250.

An automated lathe can finish a production batch in 8 hours. After running for 2 hours, it breaks down and requires 1 hour of maintenance. Once repaired, it operates at only 75% of its original speed. How many hours in total does the batch take to complete?

9 hours
10 hours
11 hours
12 hours

Explanation: In the first 2 hours, the lathe completes 2/8 = 1/4 of the batch. The remaining 3/4 is processed at 75% of the original rate, which is (1/8) × (3/4) = 3/32 per hour. The time needed for the remainder is (3/4) ÷ (3/32) = 8 hours. Adding the initial 2 hours and the 1-hour repair gives 11 hours.

A mason can build 1/24 of a compound wall per day and works 4 days a week. After 3 weeks, a second mason who builds 1/48 per day and also works 4 days a week joins him. How many weeks in total are needed to complete the wall?

4 weeks
5 weeks
6 weeks
7 weeks

Explanation: The first mason's weekly output is 4 × (1/24) = 1/6. In 3 weeks he completes 3 × (1/6) = 1/2 of the wall. The second mason's weekly output is 4 × (1/48) = 1/12. Together they produce 1/6 + 1/12 = 1/4 per week. The remaining 1/2 therefore requires (1/2) ÷ (1/4) = 2 weeks. The total is 3 + 2 = 5 weeks.

A master carpenter can build a frame in 12 days, while his apprentice would take 18 days. The master works alone for 4 days and then trains the apprentice so thoroughly that the apprentice matches the master's speed. They then work together to finish. How many days in total does the frame take?

6 days
7 days
8 days
9 days

Explanation: In 4 days, the master completes 4/12 = 1/3 of the frame. After training, the apprentice also works at 1/12 per day. Together they produce 1/12 + 1/12 = 1/6 per day. The remaining 2/3 therefore requires (2/3) ÷ (1/6) = 4 days. The total duration is 4 + 4 = 8 days.

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