Showing posts with label questions on time and work. Show all posts
Showing posts with label questions on time and work. Show all posts

Sunday, January 26, 2014

time and work questions solutions

Time and work questions solutions 

Difficulty Level - Medium

      
      1.     A can work on 1km railway track in 1 day. In how many days, will he able to complete the work on 12km railway track?

Soln: no. of days = total work / work done in 1 day
Therefore, no. of days taken = 12/1 = 12 days


      2.     A can complete the work in 15 days. What fraction of work will be completed in 1 day?

Soln.:   Let the total work is 1 unit.
Work in 1day = total work/no. of days to complete
                                    = 1/15th of work

      3.     A can do a piece of work in 3 days and B can do a piece of work in 5 days. In how many days will the work be completed if both A and B work together?

Soln.: Using formula:
                  Work done by A in 1 day = 1/3
                  Work done by B in 1 day = 1/5
                  Total work done by A and B in 1 day = 1/3 + 1/5 = 8/15
                  Therefore, no. of days to complete work by A and B together = 1/(Total work) = 1/(8/15) = 15/8 days which is less than 3 and 5

    Using shortcut/analysis/assumption
                  Let us consider the total work be 15 units (LCM of 3 and 5)
                  So work done by A in 1 day = 15/3 = 5 units
                  Similarly work done by B in 1 day = 15/5 = 3 units
                  So total work done by A and B in 1 day = 5 + 3 = 8 units
                  Therefore, no. of days to complete total work i.e. 15 units = total work/work done in 1 day = 15/8 days
       
      Note:
                a.     Work done by A and B in 1 day will always be greater than that of A and B individually
          b. No. of days taken by A and B together will always be less than that of A and B individually

      4.     A can do a piece of work in 6 days, B can do a piece of work in 4 days and C can do a piece of work in 12 days. Find the no. of days to complete the work if A, B and C work together?

Soln.: Using formula:
                  Work done by A in 1 day = 1/6
                  Work done by B in 1 day = ¼
                  Work done by C in 1 day = 1/12
                  Total work done by A, B and C in 1 day = 1/6 + ¼ + 1/12 = 12/24 = 1/2
                  Therefore, no. of days to complete work by A, B and C together = 1/(Total work) = 1/(1/2) = 2 days which is less than 4, 6, 12

      Using shortcut/analysis/assumption
                  Let us consider the total work be 24 units (LCM of 4, 6, 12)
                  So work done by A in 1 day = 24/4 = 6 units
                  work done by B in 1 day = 24/6 = 4 units
                  work done by C in 1 day = 24/12 = 2 units
                  So total work done by A, B and C in 1 day = 6 + 4 + 2 = 12 units
                  Therefore, no. of days to complete total work i.e. 24 units = total work/work done in 1 day = 24/12 = 2 days

The above Note is valid here as well.

      5.     A can do a piece of work in 6 days and B can do a piece of work in 12. Find the no. of days to complete the work if A and B work alternatively?

Soln.: Using formula:
                  Work done by A in 1 day = 1/6
                  Work done by B in 1 day = 1/12
                  Total work done by A and B working 1 day each = 1/6 + 1/12 = 3/12 = ¼
                  Therefore, 1/4th of work is done in 2days.
                  No. of days to complete total work if A and B work alternatively = 1/((1/4)/2) = 8 days

      Using shortcut/analysis/assumption
                  Let us consider the total work as 12 units (LCM of 6, 12)
                  So work done by A in 1 day = 12/6 = 2 units
                  work done by B in 1 day = 12/12 = 1 unit
                  Total work done by A and B working 1 day each = 2 + 1 = 3 units in 2 days
                  Therefore, work done in 1 day = work/no. of days = 3/2 units
                        No. of days to complete work = total work/work in 1 day = 12/(3/2) = 8 days

      6.     30 men can complete a job in 40 days. Then 25 men can complete the same job in how many days?

Soln.: As per M1D1 = M2D2
               30 * 40 = 25 * x  => x = 30 * 40/25 = 48 days

      7.   30 men can complete 1500 units in 24 days working 6hrs a day. In how many days can 18 men can complete 1800 units working 8 hrs a day?



Soln.: As per the formula  (from my earlier blog), M1D1h1/W1 = M2D2h2/W2
          => 30*24*6/1500 = 18*x*8/1800
          => x = 36 days


      8.     A and B can do a work in 10 and 15 days respectively. Then combinedly A & B, in how many days the work will be completed?

      Soln.: As per the formula  (from my earlier blog), x*y/(x + y)
               A and B together can complete the work in 10 * 15/(10 + 15) = 6 days

      9.   A can do a work in 10 and, A and B together can do a work in 6 days. In how many days B can complete the same work?


      Soln.: As per the formula  (from my earlier blog), x*y/(x - y)
               B alone can complete the work in 10 * 6/(10 - 6) = 15 days


      10.  A is twice faster than B and B can complete in 12 days alone. Find the number of days to complete if A and B together work?

            Soln.: Given B works in 12 days
      A is twice faster than B => A takes 2 times less time than B
      Therefore, A completes work in 12/2 = 6 days
            A and B together can complete in 12 * 6/(12 + 6) = 4 days