Practice Time and Work Questions for Banks, SSC CGL, RRB NTPC and Sarkari Exams.
Q31. A takes 6 days to complete a work, B takes 8 days, and C takes 12 days. If they work together, but C leaves after 2 days, how many total days will it take to complete the work?
Correct Answer:
5 days
Explanation: Total work = LCM(6, 8, 12) = 24 units.
A’s rate = 4, B’s = 3, C’s = 2.
Work in 2 days = (4 + 3 + 2) × 2 = 18 units.
Remaining work = 24 – 18 = 6 units.
A and B complete remaining work in 6/(4 + 3) = 1 day.
Total time = 2 + 1 = 5 days.
Q32. A and B are hired to complete a project. A can complete it in 40 days, and B in 60 days. However, they are paid in a ratio proportional to the amount of work they do. If A is paid ₹2400, how much will B be paid?
Correct Answer:
₹1600
Explanation: A’s work = 1/40, B’s work = 1/60. Together = 1/24.
Work ratio = A:B = 3:2.
If A gets ₹2400, B gets ₹2400 × (2/3) = ₹1600.
Q33. 12 workers can complete a task in 16 days. After working for 8 days, 4 workers leave. How many more days are required to finish the remaining work?
Correct Answer:
10 days
Explanation: Total work = 12 × 16 = 192 worker-days.
Work done in 8 days = 12 × 8 = 96 worker-days.
Remaining work = 192 – 96 = 96 worker-days.
Remaining workers = 8. Days required = 96 / 8 = 12 days.
Q34. A pipe fills a tank in 12 hours, but due to a leak, it takes 16 hours to fill. If the tank is full, how long will the leak alone take to empty the tank?
Correct Answer:
48 hours
Explanation: Rate of filling without leak = 1/12, with leak = 1/16.
Leak’s rate = (1/12 – 1/16) = 1/48.
Leak will empty the tank in 48 hours.
Q35. A can complete a task in 15 days, and B can complete it in 20 days. They start working together, but after 4 days, B leaves. How many more days will A take to finish the work?
Correct Answer:
8 days
Explanation: Total work = LCM(15, 20) = 60 units.
A’s rate = 4, B’s = 3. Together in 4 days = (4 + 3) × 4 = 28 units.
Remaining work = 60 – 28 = 32 units.
A completes it in 32/4 = 8 days.
Q36. A and B can do a work in 10 days. A alone can do it in 15 days. If they are paid ₹3000 for the work, what is B’s share of the money?
Correct Answer:
₹1200
Explanation: A’s work = 1/15, Together = 1/10.
B’s work = 1/10 – 1/15 = 1/30.
Work ratio of A:B = 2:1.
B’s share = ₹3000 × (1/3) = ₹1200.
Q37. A team of 5 men can finish a task in 15 days. After 6 days, 2 more men join the team. How many total days will they take to finish the work?
Correct Answer:
13 days
Explanation: Total work = 5 × 15 = 75 man-days.
Work done in 6 days = 5 × 6 = 30 man-days.
Remaining work = 75 – 30 = 45 man-days.
New rate = 7 men per day.
Days to finish = 45 / 7 = 6.5 ≈ 7 days.
Total time = 6 + 7 = 13 days.
Q38. A, B, and C together can do a work in 10 days. A alone can do it in 20 days, and B alone in 30 days. How long will C alone take to finish the job?
Correct Answer:
60 days
Explanation: Together, 1 day’s work = 1/10
A’s 1 day’s work = 1/20, B’s = 1/30
C’s 1 day’s work = 1/10 – (1/20 + 1/30) = 1/60
Time taken by C = 60 days.
Q39. A, B, and C can finish a work in 24, 36, and 48 days, respectively. They start working together, but C leaves after 4 days. How long will it take to complete the remaining work?
Correct Answer:
10 days
Explanation: Work done in 4 days:
A + B + C’s 1-day work = (1/24 + 1/36 + 1/48) = 1/8
Work done in 4 days = 4 × 1/8 = 1/2
Remaining work = 1 – 1/2 = 1/2
Remaining work rate of A and B = (1/24 + 1/36) = 1/14.4
Time to complete = (1/2) / (1/14.4) = 10 days.
Q40. If 8 men take 12 days to complete a job, how many men are required to complete it in 6 days?
Correct Answer:
16 men
Explanation: Total work = 8 × 12 = 96 man-days.
For 6 days, men required = 96 / 6 = 16.
Q41. Two workers A and B are paid ₹2000 to complete a task. If A can finish it in 10 days and B in 15 days, how much will A earn if they work together?
Correct Answer:
₹1200
Explanation: A’s 1 day’s work = 1/10, B’s = 1/15
Together = 1/6.
A’s share = (A’s work / Total work) × ₹2000 = (1/10) / (1/6) × ₹2000 = ₹1200.
Q42. A can complete a work in 12 days, B in 18 days, and C in 36 days. How many days will they take together?
Correct Answer:
6 days
Explanation: A’s 1 day’s work = 1/12, B’s = 1/18, C’s = 1/36
Together = (1/12 + 1/18 + 1/36) = 1/6
Time taken = 6 days.
Q43. A and B together can complete a job in 12 days. B alone takes 30 days to complete it. How long will A take to complete it alone?
Correct Answer:
20 days
Explanation: Together, 1 day’s work = 1/12
B’s 1 day’s work = 1/30
A’s 1 day’s work = 1/12 – 1/30 = 1/20
Time taken by A = 20 days.
Q44. A can do a job in 20 days, and B can do the same job in 30 days. If A and B work together for 10 days, what fraction of the work is left?
Correct Answer:
1/3
Explanation: A’s 1-day work = 1/20
B’s 1-day work = 1/30
Together, 1 day’s work = (1/20 + 1/30) = 1/12
Work done in 10 days = 10 × 1/12 = 5/6
Work left = 1 – 5/6 = 1/3.
Q45. A completes a task in 8 days. B is 50% more efficient than A. How long will B take to complete the same task?
Correct Answer:
4 days
Explanation: Efficiency of B = 150% of A.
If A’s 1-day work = 1/8, B’s 1-day work = (1/8) × (3/2) = 3/16.
Time taken by B = 16/3 = 4 days.