How to solve Time and Work problems - Tricks and Concepts

Time and Work

This chapter is useful in determining the period of time in which a given task can be completed or to determine the number of person, machines etc required to complete the given task.

TERMINOLOGY

 1.  Time: It is the duration for which a person(s) actually worked on the assigned job or it is the duration which is needed by one or more than one person to complete a job.

 2.  Work: It is the amount of total job or the part of the total assigned job actually done by the person(s).

 3.  Wages: Wages are money given to each individual for his work. Wages are distributed in proportion to the work done and in indirect proportion to the time taken by the individual.


 METHODS  

Method of MAN-DAY-HOUR

If M persons work for T hours a day for D days, then total work done (W) will be = M x D x T
⇒ W/(M x D x T) = Constant

All-in-One Formula: If M1 persons can do W1 work in D1 days working T1 hours a day with efficiency E1 and M2 persons can do W2 work in D2 days working T2 hours a day with efficiency E2, then:

   ⇒ (M1 x D1 x T1 X E1)/W1= (M2 x D2 x T2 x E2)/W2

Example: 5 men can prepare 10 toys in 6 days working 6 hrs a day. Then in how many days can 12 men prepare 16 toys working 8 hrs a day?
Solution: (5 x 6 x 6)/10 =   (12 x D x 8)/16

            ⇒ D = 3 days

Method of Fractions

 1.  More men will take less days to complete a work and less men will take more.
 2.  More men will do more work as compared to less men.
 3.  More days mean more work or we can say more work require more days.

Example: 5 men can prepare 10 toys in 6 days working 6 hrs a day. Then in how many days can 12 men prepare 16 toys working 8 hrs a day?
Solution: Remember the following Steps:

 Step 1  We need to find number of days so first write the given number of days = 6

 Step 2  In first case number of men are 5 and in second case number of men are 12, it mean more men will take less days, so multiplying fraction should be less than 1 ⇒ 5/12

 Step 3  In first case number of toys are 10 and in second case number of toys are 16, it means more toys will take more days, so fraction should be more than 1 ⇒ 16/10

 Step 4  In first case number of hours are 6 and in second case number of hours are 8, it means more hours will take less days, so fraction should be less than 1 ⇒ 6/8

⇒ Required number of days = 6 x (5/12) x (16/10) x (6/8) = 3 Days

NOTE: You don’t need to write these steps just write fractions and multiply.

Working Together

 1.  If A can do a piece of work in 'x' days and B can do it in 'y' days then A and B working together will do the same work in =  xy/(x + y) days

 2.  If A and B together can do a piece of work in 'x' days and A alone can do it in 'y' days, then B alone can do the work in =  xy/(x - y) days 

 3.  If A can do a piece of work in 'x' days, B can do it in 'y' days and C can do it in 'z' days, then A, B and C working together will do the same work in =  xyz/(xy + yz + zx) days

Points to remember

 1.  Total amount of a complete job = 1 always or 100%

 2.  If any person completes a job in 'D' days then his one day’s work will be = 1/D

 3.  Reciprocal of one day’s work of a man gives total time to complete that job alone.

 4.  Efficiency is indirectly proportional to the number of days taken to complete a work.
⇒ E x D =  constant

 5.  If 'a' men or 'b' women can do a piece of work in 'd' days then 'x' men and 'y' women together can finish the whole work in = abd/(xb + ya) days

 6.  If 'a' men or 'b' women or 'c' children can do a piece of work in 'd' days then 'x' men, 'y' women and 'z' children together finish the work in = abcd/(xbc + yac + zab) days