Time & Work concepts - Roshan Khatri, IIFT Delhi


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    This lesson is based on the event conducted by ADURO. Class was taken by Roshan Khatri, a student of IIFT Delhi.

    Work is defined as the amount of job assigned or the amount of job actually done. Problem on work are based on the application of concept of ratio of time and speed. Work is always considered as a whole or one. There exists an analogy between the time-speed-distance problems and work.

    Work = 1 ( as it is always measured as a whole) = Distance
    Rate at which work is done = speed
    Number of days required to do the work = Time

    One simple technique is using days in denominator while solving questions.
    For example, A can do a job in 3 days and B can do the same job in 6 days. In how much time they can do the job together.
    Solution : 1/3 + 1/6 = 1/2, hence 2 days is the answer. Examiner can set the question in opposite way and can ask you how much time A or B alone will take to complete the job. It is quite easy to calculate said question by putting values in equation we arrived in above question.

    You need to understand one simple concept - If A can do a job in 10 day then in one day A can do 1/10th of job.

    A take 5 days to complete a job and B takes 10 days to complete the same job. In how much time they will complete the job together ?

    A's efficiency = 20%, B's efficiency = 10%. If they work together they can do 30% of the job in a day. To complete the job they need 3.33 days.

    A is twice as efficient as B and can complete a job 30 days before B. In how much they can complete the job together ?

    Let efficiency percentage as x
    A's efficiency = 2x and B's efficiency = x
    A is twice efficient and can complete the job 30 days before B.

    So, A can complete the job in 30 days and B can complete the job in 60 days
    A's efficiency = 1/30 = 3.33%
    B's efficiency = 1/60 = 1.66%
    Both can do 5% ( 3.33% + 1.66% ) of the job in 1 day.
    So the can complete the whole job in 20 days (100/5)

    A tank can be filled in 20 minutes. There is a leakage which can empty it in 60 minutes. In how many minutes tank can be filled ?

    Method 1
    ⇒ Efficiency of filling pipe = 20 minutes = 1/3 hour = 300%
    ⇒ Efficiency of leakage = 60 minutes = 100%

    We need to deduct efficiency of leakage so final efficiency is 200%. We are taking 100% = 1 Hour as base so answer is 30 minutes.

    Method 2
    ⇒ Efficiency of filling pipe = 100/20 = 5%

    4 men and 6 women working together can complete the work within 10 days. 3 men and 7 women working together will complete the same work within 8 days. In how many days 10 women will complete this work ?

    Let number of men =x, number of women = y

    ⇒ Efficiency of 4 men and 6 women = 100/10 = 10%
    ⇒ so, 4x+6y = 10, means 4 men and 6 women can do 10% of a the job in one day.
    ⇒ Efficiency of 3 men and 7 women = 100/8 = 12.5%
    so, 3x+7y = 12.5

    By solving both equations we get, x = -0.5 and y = 2

    ⇒ Efficiency of 1 woman(y) = 2% per day
    ⇒ Efficiency of 10 women per day = 20%, So 10 women can complete the job in 100/20 = 5 days

    ⇒ Efficiency of leakage pipe = 100/60 = 1.66%
    ⇒ Net filling efficiency = 3.33%
    So tank can be filled in = 100/3.33% = 30 minutes

    You can change the base to minutes or even seconds.

    A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 30 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone ?

    ⇒ Efficiency of A and B = 1/20 per day = 5% per day      ______________ 1
    ⇒ Efficiency of B and C = 1/30 per day = 3.33% per day ______________ 2
    ⇒ Efficiency of C and A = 1/30 per day = 3.33% per day ______________ 3

    Taking equation 2 and 3 together
    ⇒ B + C = 3.33% and C + A = 3.33%
    ⇒ C and 3.33% will be removed. Hence A = B
    ⇒ Efficiency of A = B = 5%/2 = 2.5% = 1/40
    ⇒ Efficiency of C = 3.33% - 2.5% = 0.833% = 1/120
    ⇒ A can do the job in 40 days and C can do the job in 120 days he they work alone.
    ⇒ Ratio of number of days in which A and C can complete the job 1:3.

    If 4 men or 6 boys can do a task in 12 days then how many days will10 men and 3 boys take to complete the task ?

    Now carefully read the question. In the first line, 4 men or 6 boys are given but the question is asked with 10 men and 3 boys means men and boys combined. If you do this question by its normal computational method, then it will take time of about 2-3 minutes to solve. But I am giving you a trick here to solve this type of question that will solve this question in seconds. You just have to put the formula and you will get the answer.
    So we should learn the rule for this type of questions.
    Rule:- if m1 men or b1 boys does a task in d1 days then m2 men and b2 boys will do it in (m1b1d1)/(m1b2+m2b1) days
    So the solution to the above problem will be, 10 men and 3 boys will do the work in (4*6*12)/(4*3+10*6) = 24*12/(12+60) = 4 days
    This is the shortest trick you can find for this type of question.

    2 men or 5 women or 10 children can do a piece of work in 36 days. In how many days, 1 man and 1 woman or 2 children can do that work ?

    Here is the shortcut trick for this type of question.
    Let m denotes man, w denotes woman and c denotes children. The equation in the given question is 2m = 5w = 10c = 36
    Now equating men and women to children respectively, 2m = 10c = > 1m = 5c and also 5w=10c = > 1w= 2c. Putting these values in question to be answered 1m+1w+2c = ?
    5c+2c+2c=36 (putting the values of m and w shown above)
    9c=36
    So c=4
    Now multiply this value of c to the given no. of children i.e. 10*4=40 days (Ans)
    So 1 man and 1 woman and 2 children will do that work in 40 days.

    For better understanding, let us take another example.

    3 men or 4 women or 12 children can do a work in 44 days. Determine in how many days, 2 men and 3 women and 5 children can do that work ?

    3m = 4w = 12c = 44
    3m=12c
    1m=4c
    So 2m=8c (2m are asked in question)
    Also 4w = 12c
    1w=3c
    So 3w=9c
    putting these values in question to be answered
    2m+3w+5c=?
    8c+9c+5c = 44
    22c = 44
    So c = 2
    Now multiply this value of c to the given no. of children i.e. 12 * 2 = 24 days (Ans)

     


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