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Saturday, June 2, 2012

Time and Work Formula, Shortcuts


1.     Work from Days:
If A can do a piece of work in n days, then A's 1 day's work =
  1
.
n

2.     Days from Work:
If A's 1 day's work =
1
,
then A can finish the work in n days.
n

3.     Ratio:
If A is thrice as good a workman as B, then:
Ratio of work done by A and B = 3 : 1.
Ratio of times taken by A and B to finish a work = 1 : 3.

4.     No. of days = total work / work done in 1 day


5.     Relationship between Men and Work

More men         ------- can do ------->             More work

Less men         ------- can do ------->             Less work


6.     Relationship between Work and Time

More work        -------- takes------>               More Time

Less work         -------- takes------>               Less Time


7.     Relationship between Men and Time

More men        ------- can do in ------->          Less Time

Less men          ------- can do in ------->          More Time


8.     If M1 persons can do W1 work in D1 days and M2 persons can do W2 work in D2 days, then 
        

9.     If M1 persons can do W1 work in D1 days for h1 hours and M2 persons can do W2 work in D2 days for h2 hours, then

 Note:  If works are same, then M1D1h1 = M2D2h2 


10.  If A can do a work in ‘x’ days and B can do the same work in ‘y’ days, then the number of days required to complete the work if A and B work together is




11.  If A can do a work in ‘x’ days and A + B can do the same work in ‘y’ days, then the number of days required to complete the work if B works alone is



           




28 comments:

  1. For easily solving any question on work and time, one must have clear understanding of concepts. While searching google, I found this page:
    http://learnapti.com/Numerical-Aptitude/Time-and-work.aspx .

    I found this quite useful, so i am sharing this with all of you.

    ReplyDelete
  2. nice formulas.... really it will help me for my exmas.... amazing........

    ReplyDelete
  3. Thanks. Compact and helpful.

    ReplyDelete
  4. Hi, can u solve this question,

    " 12 men alone can complete a piece of work in six days, whereas 10 men and 21
    women take three days to complete the same piece of work. In how many days
    can 12 women alone complete the same piece of work? "

    ReplyDelete
    Replies
    1. Let us assume a man can do 'x' units of work and a woman can do 'y' units of work per day.
      So total work done in 1st case = 12*6*x = 72x
      Work done in 2nd case = 3*(10x + 21y) = 30x + 62y
      In both the cases, work is same as mentioned in the problem.
      => 72x = 30x+62y
      => 42x = 62y => 2x = 3y
      Let us assume, x as 3 and y as 2 to satisfy the above equation
      Total work = 72*3 = 216
      To complete 216 units of work by 12 women, they require 216/(12*2) = 9 days.

      Delete
    2. Work done in 2nd case = 3*(10x + 21y) = 30x + 62y ???

      I hope u understand dear (21*3 is 63 not 62)

      Delete
    3. i dint understand y did u multiply 12*2 in d denominator can u pls explain me

      Delete
  5. This comment has been removed by the author.

    ReplyDelete
  6. First i wanted to say thanks for easy understanding.But there is a small correction in the question no 11,
    If A can do a work in ‘x’ days and A + B can do the same work in ‘y’ days, then the number of days required to complete the work if B alone can do the work ??

    ReplyDelete
    Replies
    1. Correct, Thanks for the correction..

      Delete
  7. plz help me out to solve the questions
    if 9 men working 71/2 hrs a day can complete a work in 20 days,then in how many days will be taken by 12 men,working 6 hrs a day to finish the work?it is being given that 2 men of latter type works as much as 3 men of former type?

    ReplyDelete
    Replies
    1. Given that 2 men of latter type works as much as 3 men of former type
      => Let us assume former type completes 2 pieces of work while latter type completes 3 pieces of work each.

      So work completed in 1st case is 9 * 15/2 * 20 * 2
      If 'x' is the no. of days to complete work, work completed in 2nd case is 12 * 6 * x * 3

      As the work is same in 2 cases,
      9 * 15/2 * 20 * 2 = 12 * 6 * x * 3
      => x = 12.5 days

      Delete
  8. 6 men and 8 boys can do a price of work in 10 days while 26 men and 48 boys finish it in 2 days. 15 men and 20 boys will finish it in ???

    ReplyDelete
    Replies
    1. plzzz....tell off me how u solve it easily within few sec.

      Delete
    2. This comment has been removed by the author.

      Delete
  9. 6 men + 8 Boys = 10 days, 26 men and 48 Boys = 2 days
    60 men + 80 Boys = 52 Men + 96 Boys
    8 M = 16 B
    1 Man = 2 Boys
    15 M + 20 B = 30 B + 20 B = 50 Boys
    6 men + 8 boys = 12 Boys + 8 Boys = 20 Boys = 10 Days
    Boy Days
    20 10
    50 x
    50x = 20* 10
    x = 20*10/50 = 4 days.

    ReplyDelete
  10. Please solve this question-
    Father and mother can fill a water tank in 2 hours,Father and son in 2 and a 1/2 hours,Mother ans son in 3 hours.If all three work together in how may hours they can fill the Tank?

    ReplyDelete
    Replies
    1. This comment has been removed by the author.

      Delete
    2. 2F+2M+2S = 2 + 2 1/2+ 3
      F + M + S = ( 15/2 )/ 2
      F + M + S = 15/2 this time to fill 3 tanks
      ie F + M +S = fill a tank 15/2/3
      the answer is - 15/6 , 1 1/4 hours.

      Delete
  11. Please Solve this question for me..
    One boy can deliver newspapers on his route ub 1x1/4 hours. Another boy who takes his place one day takes 15 minutes longer. How long would it take to deliver the papers if the two boys worked together?
    I NEED THE SOLUTION URGENTLY :(

    ReplyDelete
  12. Please help me solving this, A+B = 12 days, B+C = 10 days, C+A = 15 days. A alone in how many days? (please give step by step solution)

    ReplyDelete
    Replies
    1. 2(A+B+C)=1/12+1/10+1/15.
      From above equation we will get A+B+C=1/8.
      Then for A's work=total work done by all members-work done by B&C
      =>A's 1days work=(1/8)-1/10
      =1/40.
      So A can do the work in 40 days

      Delete
  13. Karan, Kabir and Kartik can together finish a project in 4 days. Karan by himself can do it in 12 days and kabir by himself can do it in 10 days. How many days will karthik take to finish the project alone?
    pleas reply

    ReplyDelete