Time and work problems deal with the simultaneous performance involving the efficiency of an individual or a group and the time taken by them to complete a piece of work. Work is the effort applied to produce a deliverable or to complete a task.

Concept 1:

The Basic formula used to calculate days, time and efficiency is 

               Days * efficiency = Work

Example 1:

     If Ram can complete 50 work in 5days, then the efficiency will be 50/5=10

     i.e Ram eff=10 , Ram can complete 10 work in a day.

Example 2:

       If there are total 120 work and A can finish the work in 15 days and B can finish the work in 10days.

       Then Efficiency of A will be 120/15= 8(i.e A can finish 8 unit of work in a day)

       Then Efficiency of B will be 120/10= 12(i.e B can finish 10 unit of work in a day)

Concept 2:

The wages will be distributed always in terms of efficiencies.

Example :

     Suppose 2400rs has to be divided among A and B  for completing a work and Efficiency of A:B=12:8

     Then A will get 2400 * 12/(12+8) = 1440rs

     and B will get 2400 * 8/(12+8) = 960rs

Concept 3:

M1 men can do a piece of  W1 work H1 hours per day in D1 days. the number of days will be required to complete the work by M2 men are working H2 hours per day is given by

             ( M1*D1*H1 ) / W1 = ( M2*D2*H2 ) / W2

Example:

24 men can do a piece of work 8 hours per day in 50 days. how many days will required to complete the work by 16 men, are working 6 hours per day ?

       a. 55      b. 50       c. 75       d. 100

Sol: M1=24, M2=16  &  D1=50, D2=?

        H1=8, H2=6    &    W1=W2=1

       So, D2=[24*50*8]/(6*16)=100 days

A can do a piece of work in 12 days, B can do the same work in 24 days. If they are working together. In how many days the work will be completed?

a) 8 days                       b) 6 days                       c) 10 days                     d) 9 days

Solution:

A’s 1 day’s work = 1 / 12, B’s 1 day’s work = 1 / 24

(A + B)’s 1 day’s work = (1 / 12) + (1 / 24) = (2 + 1) / 24 = (1 / 8)

⸫ A and B together will complete the work in 8 days.

Answer: a