Time & Work Level-3 Quiz-2

1. A contractor employed some workers to finish a certain project in a specified time. After a few days of work, he realized that the actual time would overshoot the scheduled time by 25%. So, he increased the workforce by a third and managed to finish the project on time. Find the fraction of work that was completed by the time the additional workers were employed.

2. In the previous question, What fraction of the scheduled time is the time after which the additional workers were employed?

3. A cistern can be filled by two pipes in 8 min and 12 min respectively. Both pipes are opened together for a certain time but due to some defects, only 5/6 th of full quantity of water flows through the former and only 3/4 th through the latter. The defects are detected and rectified. The cistern is filled in 2 min from that moment. How long was it before the defects were rectified?

4. A, B and C are three pipes which are attached to a tank. A and B fill the tank in 20 and 30 mins respectively and C empties it in 15 min. If A, B, C are opened in that order for 2 min each till the tank gets filled, then how many minutes will it take for the tank to get filled?

5.

In a factory, there are two machines $A$ and $B$ producing toys. They respectively produce $60$ and $80$ units in one hour. $A$ can run a maximum of $10$ hours and $B$ a maximum of $7$ hours a day. The cost of their running per hour respectively amounts to $2,000$ and $2,500$ rupees. The total duration of working these machines cannot exceed $12$ hours a day. If the total cost cannot exceed Rs. $25,000$ per day and the total daily production is at least $800$ units, then formulate the problem mathematically.

6. A contractor employed 20 men to complete a project in 50 days. After 30 days, he observed that only 50% of the work had been completed. How many more men should be employed to complete the work in time?

7. In the previous question, If the work is increased by 20% of the original and still the contractor wants to finish it within 50 days, then atleast how many more men need to be employed?

8. A garrison had provisions for 1500 men for 30 days. After some days, 300 more men joined the garrison. The provisions lasted for a total of 26 days from the beginning. After how many days did the new men join?

9. A task is assigned to a group of twenty men, not all of whom have the same capacity to work. Every day exactly two men out of the group work on the task, with no same pair of men working together twice. Even after all the possible pairs have worked once, all the men together had to work for exactly one more day to finish the task. Find the number of days required for all the men working together to finish the task.

10.