Fill in the blanks:
A can complete a work in 12 days, and B can complete the same work in 18 days. If they work together, they will complete the work in ___ days.

7.2 days (LCM(12,18) = 36; A’s rate = 36/12 = 3, B’s rate = 36/18 = 2; Total rate = 3+2 = 5; Work done in 36/5 = 7.2 days)

True or False: If the number of workers doubles, the time required to complete the work is always reduced by half.

False (Only true if efficiency remains constant and there are no diminishing returns in productivity)

Riddle: A tap fills a tank in 6 hours, and a leak empties the tank in 8 hours. If both are open together, the tank will be filled in ___ hours.

24 hours (Filling rate = 1/6, Leak rate = 1/8; Net rate = 1/6 - 1/8 = 1/24 → Tank fills in 24 hours)

Fill in the blanks:
A can do a job in 15 days, and B can do the same job in 10 days. If A and B work together for 5 days, the remaining work is ___ fraction of the total work.

1/3 (A’s rate = 1/15, B’s rate = 1/10, Combined rate = (1/15 + 1/10) = 1/6; Work done in 5 days = 5/6; Remaining = 1 - 5/6 = 1/3)

True or False: If A and B can together finish a work in 10 days, and A alone can do it in 16 days, then B alone can do it in 20 days.

False (Using formula 1/B = 1/10 - 1/16 = 3/80 → B alone takes 80/3 days ≈ 26.67 days, not 20 days)

Fill in the blanks:
A alone can finish a work in 8 days. B is 50% more efficient than A. B alone can finish the same work in ___ days.

5.33 days (or 16/3 days) (If B is 50% more efficient, his rate is 1.5 × A’s; Time = 8/1.5 = 16/3 ≈ 5.33 days)

Riddle: Three pipes A, B, and C can fill a tank in 12 hours, 15 hours, and 20 hours, respectively. If all three are opened together, the tank will be filled in ___ hours.

5.45 hours (or 60/11 hours) (Rates: A = 1/12, B = 1/15, C = 1/20; Total rate = (1/12 + 1/15 + 1/20) = 11/60; Time = 60/11 ≈ 5.45 hours)

True or False: If three workers can complete a task in 9 days, then the number of days required for one worker to complete the same task alone is 27 days.

True (Total work = 3 workers × 9 days = 27 worker-days; Time for 1 worker = 27 days)

Fill in the blanks: 
A and B can finish a work in 20 days, B and C can finish it in 30 days, and A and C can finish it in 40 days. The time taken by A, B, and C together to finish the work is ___ days.

16 days (Using the equation 1/A + 1/B + 1/C = (1/20 + 1/30 + 1/40) = 1/16 → Work done in 16 days)

A group of 4 men can complete a work in 16 days. If 2 more men join, the work will be completed in ___ days.

8 days (More workers → Less time; Time = 4 × 16 / 6 = 8 days)

Fill in the blanks:

A, B, and C together finish a work in 10 days. If A alone takes 20 days and B alone takes 30 days, then C alone will take ___ days.

60 days (Using 1/C = 1/10 - 1/20 - 1/30 = 1/60 → C alone takes 60 days)

True or False: If a task takes 12 hours with 6 workers, it will always take 6 hours with 12 workers.

False (Only true if efficiency remains constant and no other factors affect productivity)

Riddle: A can do a work in 9 days, and B in 18 days. If they work together but B leaves after 3 days, the total time required to complete the work is ___ days.

6 days (A’s rate = 1/9, B’s rate = 1/18; Combined for 3 days = (1/9 + 1/18) × 3 = 1/2; Remaining work = 1/2; A alone = 1/2 × 9 = 4.5 days; Total = 3 + 4.5 = 6 days)

Fill in the blanks:

Two pipes fill a tank in 12 min and 18 min, while a third pipe empties it in 36 min. The net time to fill the tank when all three work together is ___ min.

9 min (Rates: 1/12 + 1/18 - 1/36 = 1/9; Time = 9 min)

True or False: If A is twice as fast as B, and both together take 16 days, then A alone will take 24 days.

False (Using formula: If A = 2B, then 1/A + 1/B = 1/16 → 1/2x + 1/x = 1/16 → x = 24; A = 12 days, not 24)