Time and Work Shortcuts

TIME AND WORK SHORTCUTS Following are the most popular types based on which questions are asked in various examinations’. 1. Time taken to do a certain job by a certain number of workers 2. The change in the number of hours required to do a job if the number of workers is changed. 3. The number of hours required to do the job by different workers if their speeds are different. 4. Problems on wages earned by various workers executing a certain work in proportion with the amount of work done by each worker 5. Work done by various people in alternate intervals 6. Time taken by pipes/taps/leakages to fill/empty tanks/cisterns. There are certain points that are to be kept in mind while doing problems. They are:1. A person does the same amount of work everyday(unless specified in the problem). Note a. If A can do a piece of work in ‘n’ days, then the amount of work done by A in one day is 1/n. b. Conversely, if A’s 1 day’s work=1/n, then A can finish the work in n days. 2. If there are more than one person involved carrying out the work collectively, it is assumed that the working capacity of each person is the same unless specified in the problem. 3. MANDAYS: If ‘m’ men worked for ‘d’ days to finish a job, then we can say m*d mandays are required to finish the job. Mandays required to finish a job remains constant while number of men or number of days needed to complete the jobs can vary. In general we can say that if w1 work is done by m1 men working h1 hours per day in d1 days and w2 work is done by m2 men working h2 hours per day in d2 days then m1d1h1w2=m2d2h2w1 Approach to Question 1. Calculate the time taken by two persons working together to finish a work A can complete a piece of work in 10 days which B alone can complete in 12 days. In how many days can they finish the work if they both work together? T=(XY)/(X+Y) where X and Y are the time taken by A and B 2. Calculate the time taken by three persons working together to finish a wok A can complete a piece of work in 5 days alone which B can complete in 6 days. If C who can complete the work in 12 days joins them, how long will they take to complete the work? T=(XYZ)/(XY+YZ+ZX) where X, Y and Z are the time taken by A, B and C individually 3. If one worker is ‘m’ times as efficient as another worker and takes ‘d’ days less than the other person, then in how many days can both finish the work working together? A is thrice as efficient as B and takes 60 days less than B for finishing a job. Find the time in which they can finish the work together. T=(m*d)/(m^2 –1) 4. One pipe can fill a cistern in T1 mins and another pipe in T2 mins. If both the pipes are opened together, find the time taken to fill the cistern.A pipe can fill a cistern in 30 min and another can fill it in 40 min. If both are opened simultaneously, find the time taken to fill the cistern T=(T1*T2)/(T1-T2) 5. One tap can fill a cistern in T1 mins and another tap can empty it in T2 mins. If both the taps are opened together, find the time taken to fill the cistern A cistern is filled by a tap A in 10 hours and emptied by tap B in 12 hours. If both the taps are opened simultaneously, find the time taken to fill the cistern. T=(T1*T2)/(T2-T1)