Time & Work Primer - Ravi Handa


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    A work can be done by 4 people in 32 days. How many more days will it take if 16 people join them two days after starting?

    In questions on 'Time and Work', it is a good idea to first calculate the total amount of work that is to be done. Often, you will find it terms of Man-Days.
    In this particular question, we are given that 4 men take 32 days to complete the work
    => Total amount of work = 4 * 32 = 128 man-days
    In the first two days, the 4 people will accomplish work worth = 4 * 2 = 8 man-days
    Work remaining = 128 - 8 = 120 man-days
    Total number of men that are now available to finish the work = 4 + 16 = 20 men
    Number of days required by these men to finish the work = 120/20 = 6 days

    6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10 times the amount of work if they work for 25 days of 8 hours?

    Total amount of work that needs to be done = 6 men * 30 days * 9 hours = 1620 Man-Hours
    10 times the amount of work would be 16200 Man-Hours
    The men are now working for 25 days and 8 hours on each day
    => Every man is working for 25 * 8 = 200 hours
    Number of men required = 16200 / 200 = 81 Men

    A and B can finish a work together in 12 days, and B and C together in 16 days. If A alone works for 5 days and then B alone continues for 7 days, then remaining work is done by C in 13 days. In how many days can C alone finish the complete work?

    Let us say that A takes 'a' days to finish the work, B takes 'b' days to finish the work and C takes 'c' days to finish the work.
    => A in one day will do 1/a units of work, and similarly B and C will do 1/b and 1/c units of work in one day.
    We are given that A and B together can finish the work in 12 days
    => 1/a + 1/b = 1/12
    Similarly, we are also given that B and C together can finish the work in 16 days
    => 1/b + 1/c = 1/16
    We also know that the work can be finished if A works for 5 days, B for 7 Days and C for 13 days
    => 5/a + 7/b + 13/c = 1
    So, we have three equations and three variables. We can solve them to get the individual values of 'a', 'b' and 'c'. We are asked to find out in how many days would C alone finish the work. So, we are asked to find out the value of 'c'.
    If we multiply the first equation with 5 and the second equation with 2 and add them up, we will get
    5(1/a + 1/b) + 2(1/b + 1/c) = 5/12 + 2/16
    => 5/a + 7/b + 2/c = (20 + 6)/48 = 26/48
    => 5/a + 7/b + 2/c = 13/24
    If we subtract the above equation from the third equation, we will get
    (5/a + 7/b + 13/c) - (5/a + 7/b + 2/c) = 1 - 13/24
    => 11/c = 11/24
    => c = 24
    So, we can say that C alone will take 24 days to complete the work.

    If 3 men completes work in 7 days how many days will 5 men take?

    n this particular question, we are given that 3 men take 7 days to complete the work
    => Total amount of work = 3 * 7 = 21 man-days
    We now have 5 men available with us.
    Number of days required by these men to finish the work = 21/5 = 4.2 days

    If 21 men take 30 days to a complete a work. In how many how days will 45 men complete the work?

    In this particular question, we are given that 21 men take 30 days to complete a work
    => Total amount of work = 21*30 = 630 man-days
    We now have 45 men available with us.
    Number of days required by these men to finish the work = 630/45 = 14 days

    Alex takes twice as much time as Andy and thrice as much as Viney to finish the work. Together they finish in 1 day. What is the time taken by Alex to finish the work?

    Let us say that Viney takes '2x' hours to finish the work
    => Alex will take thrice as much, so Alex will take '6x' hours to finsih the work.
    => Andy will take half of what Alex takes, so Andy will take '3x' hours to finish the work.
    Together, they finish the work in 24 hours.
    => 1/2x + 1/3x + 1/6x = 1/24
    => (3 + 2 + 1)/6x = 1/24
    => 1/x = 1/24
    => x = 24 hours = 1 day
    Alex takes 6x hours or 6 days to finish the job.

    A and B can complete a job in 30 and 20 days respectively. They start working together and B leaves 5 days before the work is finished. In how many days is the total work finished?

    Method 1:
    A and B can do the job in 30 and 20 days individually, so together they will take 30 * 20/(30 + 20) = 600/50 = 12 days.
    The work that A can do in 5 days is 1/6th. So, A left when 5/6th of the work was done or A left after (5/6) * 12 = 10 days
    Total time taken = 10 + 5 = 15 days.

    Method 2:
    A and B can do the job in 30 and 20 days. A worked for the complete period of 'd' days, whereas B worked for 'd-5' days to finish the job
    => d/30 + (d-5)/20 = 1
    => 2d + 3d - 15 = 60
    => 5d = 75
    => d = 15 days

    Aslam, Zahid and Ali can do a work respectively in 15 days, 6 days and 10 days. How many days three men will spend together to finish three times that work?

    In 1 day, working together they will do
    1/15 + 1/6 + 1/10 = (2 + 5 + 3)/30 = 10/30 = 1/3 rd of the work
    So, in 3 days they will finish the work.
    To finish three times the work, they will need 3*3 = 9 days


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