Practice Time and Work Questions for Banks, SSC CGL, RRB NTPC and Sarkari Exams.
Q16. A and B can finish a task in 10 days. A alone takes 15 days. If they are paid ₹3,000 for the work, how much should A receive based on the work done?
Correct Answer:
₹1,800
Explanation: Work rates: A = 1/15, A + B = 1/10.
B’s rate = 1/10 – 1/15 = 1/30.
Work ratio = 1/15 : 1/30 = 2 : 1.
A’s share = ₹3,000 × 2/3 = ₹1,800.
Q17. A can do a job in 24 days, and B can do the same job in 36 days. If A and B work together but are paid in proportion to the work done, and they receive ₹10,800, how much will B get?
Correct Answer:
₹3,600
Explanation: Work rates: A = 1/24, B = 1/36.
Work ratio = 36 : 24 = 3 : 2.
B’s share = ₹10,800 × 2/5 = ₹4,800.
Q18. A and B are hired to complete a job. A can complete the task in 18 days, while B can do it in 12 days. If they are paid ₹6,000 for the entire job, what is the ratio of their earnings?
Correct Answer:
3:2
Explanation: Work rates: A = 1/18, B = 1/12.
Ratio of work = 1/18 : 1/12 = 2 : 3.
Therefore, A earns ₹2,400, and B earns ₹3,600.
Q19. A and B can complete a task in 24 days. B and C can complete it in 30 days. A and C can complete it in 40 days. How many days will it take for A, B, and C to complete the work together?
Correct Answer:
10 days
Explanation: Combined work rate: (A + B)’s rate = 1/24, (B + C)’s = 1/30, (A + C)’s = 1/40.
Adding all: (A + B + C)’s 2-day work = (1/24 + 1/30 + 1/40) = 1/10.
(A + B + C)’s 1-day work = 1/20.
Time = 1 / (1/20) = 15 days.
Q20. A can do a job in 20 days, B can do it in 30 days, and C can do it in 60 days. They start working together, but A leaves after 5 days. How many days will it take for B and C to complete the remaining work?
Correct Answer:
8 days
Explanation: Total work = LCM(20, 30, 60) = 60 units.
A’s rate = 3 units/day, B’s = 2 units/day, C’s = 1 unit/day.
Work done in 5 days = (3 + 2 + 1) × 5 = 30 units.
Remaining work = 60 – 30 = 30 units.
Rate of B and C together = 2 + 1 = 3 units/day.
Time = 30/3 = 10 days.
Q21. A can do a job in 15 days, B can do it in 20 days, and C can do it in 30 days. They work together for 6 days, and then A leaves. How many more days will B and C take to finish the remaining work?
Correct Answer:
6 days
Explanation: Total work = LCM(15, 20, 30) = 60 units.
A’s rate = 4, B’s = 3, C’s = 2. Together, 1-day work = 9 units.
Work done in 6 days = 9 × 6 = 54 units.
Remaining work = 60 – 54 = 6 units.
Rate of B and C = 3 + 2 = 5 units/day.
Time = 6/5 = 1.2 days.
Q22. A group of workers was supposed to complete a task in 20 days. However, due to 4 workers leaving after 5 days, the work took a total of 25 days. How many workers were originally in the group?
Correct Answer:
15
Explanation: Let the original number of workers be N, and work=Nx20.
Work done in the first 5 days = 5N.
Remaining work = 15N, completed in 20 days by N-4.
15N = 20 x (N-4). Solve N = 15
Q23. A cistern has two pipes. Pipe A can fill it in 12 hours, and Pipe B can fill it in 16 hours. Pipe C can empty it in 24 hours. If all three pipes are opened together, how long will it take to fill the cistern?
Q24. A job is assigned to two workers A and B, who can finish it in 16 and 24 days, respectively. However, they work on alternate days, with A starting first. How many total days will it take to complete the work?
Correct Answer:
21 days
Explanation: A + B’s 2-day work = (1/16 + 1/24) = 5/48.
Total cycles in 20 days: ( 48/15 = 21 Days!..
Q25. Three workers A, B, and C can complete a task in 12 days. A alone takes 18 days, and B alone takes 36 days. How long will it take C to complete the task alone?
Correct Answer:
30 days
Explanation: Combined rate = 1/12, A’s = 1/18, B’s = 1/36.
C’s rate = (1/12 – 1/18 – 1/36) = 1/36.
Time for C alone = 1/(1/36) = 36 days.
Q26. A contractor hires 10 men to finish a task in 30 days. After 15 days, he realizes only half the work is done. How many more men should he hire to complete the task on time?
Correct Answer:
10 men
Explanation: Total work = 10 × 30 = 300 man-days.
Work done in 15 days = 10 × 15 = 150 man-days.
Remaining work = 150 man-days in 15 days.
Required workforce = 150 / 15 = 20 men. Additional = 20 – 10 = 10 men.
Q27. A machine produces 10,000 widgets in 5 hours, but its efficiency drops by 20% every 2 hours. How many widgets will it produce in 10 hours?
Q28. A and B can complete a task in 18 days, B and C in 24 days, and C and A in 36 days. How long will A, B, and C take together to finish the work?
Correct Answer:
12 days
Explanation: (A + B)’s 1 day’s work = 1/18, (B + C)’s = 1/24, (C + A)’s = 1/36.
Adding: 2(A + B + C)’s work = (1/18 + 1/24 + 1/36) = 1/8.
A + B + C’s 1 day’s work = 1/16.
Time to complete = 16 days.
Q29. Three workers A, B, and C are paid ₹4500 for completing a task. A and B together can complete the task in 15 days, B and C together in 10 days, and A and C together in 12 days. Find C’s share of the payment.
Correct Answer:
₹1500
Explanation: Total work: (A + B + C)’s 1 day’s work = (1/15 + 1/10 + 1/12)/2 = 1/8.
A’s work = 1/8 – 1/10, B’s = 1/8 – 1/12, C’s = 1/8 – 1/15.
Proportions: A:B:C = 1:1:3.
C’s share = ₹4500 × (3/5) = ₹1500.
Q30. If 9 women can complete a job in 12 days, and 12 children can complete it in 18 days, how many women and children working together can complete it in 6 days?
Correct Answer:
8 women and 8 children
Explanation: 9 women’s work = 12 days → Total work = 108 woman-days.
Similarly, 12 children’s total work = 216 child-days.
1 woman = 2 children.
Required work for 6 days = 108 woman-days / 6 = 18 woman-equivalents.
8 women + 8 children = 16 women + 2 women = 18 woman-equivalents.