Time and Work Questions for CAT

A group of workers of Prashant Engineering Works was assigned a work of assembling 360 small transformers, in a certain number of days. By assembling 4 transformers more than what they were assigned to assemble every day, they finished the work 1 day earlier. For how many days did the group work?

$A$ and $B$ undertake to do a piece of work for ₹ 100. $A$ can do it in 5 days and $B$ can do it in 10 days. With the help of $C$, they finish it in 2 days. How much should $C$ be paid for his contribution?

How many women are needed to help one man and one kid finish a certain task in 3/5 of a day, given that a man, a woman, and a kid can complete the work alone in 6, 15, and 10 days respectively?

Two pipes P and Q can fill a tank in 10 hours and 15 hours respectively. How long will it take if both pipes are opened together?

Two pipes, A and B, are connected to a tank. Pipe A is only for filling, while pipe B can either fill or empty at the same rate. When both A and B are filling, the tank fills in p hours. When B is emptying while A is filling, the tank fills in 4p hours. What is the ratio of the flow rates of A and B?

Three pipes are connected to a tank: two are filling pipes and one is an emptying pipe. The filling pipes can fill the tank individually in 8 hours and 12 hours, while the emptying pipe can empty it in 6 hours. The filling pipes start filling the empty tank, and when half of the tank is filled, the emptying pipe was supposed to be opened. However, due to a glitch, the emptying pipe was opened when only one-fourth of the tank was filled. How much delay occurred in completely filling the tank because of this?

A tank with a capacity of 6400 litres is connected to three taps with different filling rates. Tap A fills 2 buckets in 12 minutes, Tap B fills 8 buckets in 16 minutes, and Tap C fills 12 buckets in 30 minutes (all buckets are the same size). When the tank is full, all taps are opened simultaneously, but Tap A and Tap B drain the tank while Tap C fills it. The tank is emptied in 50 hours. What is the capacity of each bucket (in litres)?

A teacher took all 150 of his students to a shooting range, where each shot cost Rs. 10. Eighteen of his students fired three shots each, and 40 students took at least two shots each. The teacher spent a total of Rs. 2000, and it is known that no student fired more than three shots. How many students did not fire a single shot?

The work done by a man, woman, and child is in the ratio of 3:2:1. If the daily wages of 20 men, 30 women, and 36 children total Rs. 78, what will be the wages for 15 men, 21 women, and 30 children over 18 weeks?

Bibhor requires 3 hours to collect the same amount of water that Ahmed can collect in 2 hours. Deepak takes 5 hours to collect the same amount of water that Bibhor can collect in 4 hours. If they all work together, the tank fills in 20 hours. How long would it take Bibhor to fill the tank by himself?

$A, B$ and $C$ working together completed a job in 10 days. However, $C$ only worked for the first three days when $37 / 100$ of the job was done. Also, the work done by $A$ in 5 days is equal to the work done by $B$ in 4 days. How many days would be required by the fastest worker to complete the entire work?

A car factory had a specific number of workers who produced a certain number of cars daily. However, due to the nationwide lockdown, some workers returned to their hometowns. During the following unlock phases 1, 2, 3, and 4, each lasting 10 days, the factory was allowed to operate with 20%, 40%, 60%, and 80% of the remaining workers, respectively. If the average daily output during these phases is 40% of the pre-lockdown output, what percentage of workers returned to their hometowns?

A fill pipe can fill a tank in 30 hours, while a drain pipe can empty it in 15 hours. If a system of n pipes, both filling and draining, can fill an empty tank in 5 hours, what could be the possible value of n from the options below?

Two taps fill a cistern in 6 hours and 8 hours. A third tap empties it in 12 hours. If all three are opened together, how long will it take to fill the cistern?

X, Y, and Z can finish a task in 10, 15, and 20 days individually. They follow a 3-day work pattern: Day1: X+Y, Day2: Y+Z, Day3: X+Z, repeating until completion. Find the fraction of work done by Z.

Sam takes twice as much time as Tom to complete a project. Tom and Tim together can complete the project in one-half the time Sam takes alone. Also, Sam takes 5 days more than the three of them working together. How many days will Tim take to finish the project alone?

Asha and Bhanu can together complete a task in 20 days. After 8 days of working together, Asha's efficiency drops by 25%. They complete the task 2 days later than planned. If Bhanu had worked alone after Asha's efficiency dropped, how many days would he have taken to complete the remaining work?

A fill pipe can fill a tank in 20 hours, while a drain pipe can empty it in 30 hours. If a combination of n pipes (both fill and drain) can fill the tank in exactly 5 hours, which of the following values for n are possible (multiple options may be correct)? 32, 54, 29, 40

A, B, and C can do a piece of work individually in harmonic progression. C takes 3 times as much time as A to finish the job. If A works 6 days, B works 4 days, and C works 12 days to complete the remaining work, how many days will B take to finish the work alone?

Four friends, Arijit, Bhole, Chetan, and Diljit, can complete a wall in 140, 56, 40, and 35 days, respectively. One friend, upset with the others, decided to sabotage the wall at the same rate he would have built it. Two friends, including the saboteur, were assigned to work on the wall. If only these two had worked, the task would have taken 90-100 days. However, with one more friend joining them, the work was finished in 28 days. Which friend went rogue?