Explore key concepts of time and work with scenarios on pipes, worker efficiency, and meeting project deadlines. This quiz sharpens your understanding of rate problems and real-world calculations in work and flow situations.
Two pipes, A and B, can fill a tank in 6 hours and 8 hours respectively. If both are opened together, how long will it take to fill the tank?
Explanation: When both pipes work together, their rates are added. Pipe A fills 1/6 per hour and Pipe B fills 1/8 per hour; combined, they complete (1/6 + 1/8) = 7/24 of the tank per hour. Thus, the time to fill the tank is 24/7 hours, which is approximately 3 hours and 25 minutes. The other options are incorrect: 7 hours, 4 hours and 48 minutes, and 5 hours and 10 minutes do not correspond to the correct combined rate calculation.
Worker X can complete a task in 12 days, while Worker Y is 50% more efficient than X. In how many days can Y complete the same task alone?
Explanation: Since Y is 50% more efficient, Y can do 1.5 times the work of X in the same period. This means Y needs only 2/3 the time X needs: 12 × (2/3) = 8 days. 12 days represents X's time, and 18 or 16 days are distractors that either confuse efficiency with required time or ignore the percentage increase.
A pipe can fill a cistern in 5 hours. An outlet at the bottom can empty it in 8 hours. If both are opened simultaneously, in how many hours will the cistern be filled?
Explanation: The net rate is 1/5 (filling) minus 1/8 (emptying). That’s (8-5)/40 = 3/40 per hour. Filling the cistern takes 40/3 hours or 13 hours and 20 minutes. The other options are incorrect because they are either based on adding times instead of rates or random approximations not derived from the actual rates.
If 5 workers can complete a project in 24 days, how many workers are needed to complete it in 10 days, assuming all work at the same rate?
Explanation: Work done is inversely proportional to the number of workers when time is fixed. 5 workers × 24 days = 120 worker-days; to finish in 10 days: 120/10 = 12 workers. Options such as 15, 9, or 8 workers either misapply proportions or involve mathematical errors in the worker rate calculation.
A team must finish a job in 18 days, but after 10 days, only 50% is done. To meet the original deadline, by what factor must their rate increase?
Explanation: After 10 days and 50% completion, 50% remains for 8 days. Their current rate is 5% per day, but to finish in 8 days, they need to do 50%/8 = 6.25% per day, which is exactly double. Other options overestimate or underestimate the increase needed – quadrupling or tripling the rate would finish much earlier, while one and a half times would not be fast enough.