Work and Time

Work and Time Definition

• 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 and proportional.
• Work is always considered as a whole or one. There axists an analogy among the time-speed-distance and work.
  
  Above mentioned definition of work throws light on three important points.
  1. Work = 1 (as it is always mesured as a whole) = distance
  2. Rate at which work is done = speed.
  3. Number of days required to do the work = time

Important Formula

If $M_1$ person can do $W_1$ work in $D_1$ days and If $M_2$ person can do $W_2$ work in $D_2$ days, then it is a general formula in the relationship of $$M_1 D_1 W_1=M_2 D_2 W_2$$ If it includes the working hours $T_1$ and $T_2$ in above statement, then the relationship will be : $$M_1 D_1 W_1 T_1=M_2 D_2 W_2 T_2$$ If efficiency $E_1$ and $E_2$ of the persons also included in above statement then the relationship will be : $$M_1 D_1 W_1 T_1 E_1=M_2 D_2 W_2 T_2 E_2$$

1. Work from days :

If A can do a piece of work in $n$ days, then A's 1 day's work $ =\dfrac{1}{n}$

2. Days from Work :

If 1 day work of A is $=\dfrac{1}{n}$, then A can finish the work in $n$ days.

3. If a person can do a work in D days, then number of man required to complete the work = $M\times D$

4. Ratio :

If A is thrice as good a workman as B, then :

• Ratio of work done by A and B = 3 : 1
• Ratio of time taken by A and B to finish a work = 1 : 3
  
  

5. If A is $x$ times as good a workman as B, then he will take $\dfrac{1}{x} th$ of the time by B to do the same work.

6. A and B can do piece of work in x and y days respectively, then working together, they will take $\dfrac{xy}{x + y}$ days to finish the work and in one day, they will finish $\dfrac{x + y}{xy}$ $th$ part of work.

7. If A, B and C can do a work in x, y and z days respectvely and all work together then, they can finish the work in $$\frac{xyz}{xy+yz+zx}\; days.$$ 8. If A is R % more effcient than B,

• Work done by A : work done by B = 100 - R : 100
• Time Taken by A : Time Taken by B = 100 : 100 - R

Illustraion 1:

• Ramesh takes12 days to finish a work alone, while Suresh takes 6 days to finish the same work. What is the ratio of their efficiency and who is less efficient ?
  
  

Solution : -
Since Ramesh takes more time than Suresh to finish the same work, hence Ramesh is less efficient or $$efficiency\;of\;Ramesh=\frac{100}{12}=8.33$$ $$efficiency\;of\;Suresh=\frac{100}{6}=16.66$$ $$Ratio\;of\;efficiency\;of\;Ramesh:Suresh=\frac{1}{12}:\frac{1}{16}=1:2$$ Hence, Suresh is twice efficient than Ramesh.

Illustraion 2:

• Dinesh and Ramu can complete a work in 12 and 6 days respectively. Find the time taken by them when Dinesh and Ramu worked together ?

Solution : -
$$Time\;taken\;by\;both=\frac{12\times6}{12+6}$$ $$=\frac{72}{18}=4\;days$$