Time & Work
Work is always considered as an entire value or one. There exists an analogy between the timespeeddistance problems and work. Work based problems are more or less related to time speed and distance.
Important Formulae:1) Work from days:
If a person can do a work in 'n' days, then person's 1 day work = 1 / n
2) Days from work:
If a person's 1 day work is equal to 1/n , then the person can finish the work in 'n' days.
3) Numer of Days =  Total Work 
Work Done in 1 Day 
Quick Tricks & Tips:1) Ratio:If 'A' is 'x' times as good a workman as 'B', then
a) Ratio of work done by A & B in equal time = x: 1
b) Ratio of time taken by A & B to complete the work = 1: x. This means that 'A' takes (1/x
^{th}) time as that of 'B' to finish same amount of work.
For example,if A is twice good a workman as B, then it means thata) A does twice as much work as done by B in equal time i.e. A:B = 2:1
b) A finishes his work in half the time as B
2) Combined Work:a) If 'A' and 'B' can finish the work in 'x' & 'y' days respectively, then
(A + B)'s one day work =  1  +  1  =  (x + y) 
x  y  xy 
Together, they finish the work in  xy  days. 
(x + y) 
b) If 'A', 'B' & 'C' can complete the work in x, y & z days respectively, then
(A + B+ C) 's 1 day work =  1  +  1  +  1  =  (xy + yz + xz) 
x  y  z  xyz 
Together, they complete the work in  xyz  days. 
xy + yz + xz 
c) If
A can do a work in 'x' days and if the same amount of work is done by
A & B together in 'y' days, then
(A+B)'s one day work =  1 
y 
B's one day work =  1  –  1  =  x – y 
y  x  xy 
So, 'B' alone will take  xy  days. 
x – y 
d) If
A & B together perform some part of work in
'x' days,
B & C together perform it in
'y' days and
C & A together perform it in
'z' days, then
(A + B)'s one day work =  1 
x 
(B + C)'s one day work =  1 
y 
(C + A)'s one day work =  1 
z 
1  +  1  +  1  = 2(A+B+C)'s 1 one day work 
x  y  z 
Now, we have at hand (A + B + C)'s one day work =   1  +  1  +  1   x  y  z 

2 

(A+ B+ C) will together complete the work in   days 
2 
 1  +  1  +  1   x  y  z 

If
A works alone, then
deduct A's work from the
total work of B & C to find the
time taken by A alone.For A working alone, time required =A's work  (A+B+C)'s combined work
=  
2 
 1  –  1  +  1   x  y  z 

=  2xyz  days 
[xy + yz – zx] 
Similarly,
 If B works alone, then time required =  2xyz 
(– xy + yz + zx) 
 If C works alone, then time required =  2xyz 
(xy – yz + zx) 
3) Man Work Hour related problems:Remember that  M D H  = Constant 
W 
where,
M: Number of Men
D: Number of Days
H: Number of Hours
W: Amount of Work done
If men are fixed, work is proportional to time. If work is fixed , time is inversely proportional to men. Thus,
Once you have understood the following simple things, this chapter will become extremely easy for you.a) Work and time are directly proportional to each other
b) Number of men and time are inversely proportional to each other
c) And, work can be divided into equal parts i.e. if a task is finished in 10 days, in one day you will finish (1/10
^{th}) part of the work.
Questions Variety:Type 1: Efficiency of two or more workers is give separately. Find how much time would they take to finish the work together.
Examples:Q 1. Reema can complete a piece of work in 12 days while Seema can the same work in 18 days. If they both work together, then how many days will be required to finish the work?
a. 6 days
b. 7.2 days
c. 9.5 days
d. 12 days
View solutionCorrect answer : (b)
Hint:
(A + B)'s one day work =  1  +  1  =  (18 + 12)  =  30  =  1 
12  18  (12 x 18)  216  7.2 
Together, A & B will finish the work in 7.2 days.
Q 2. If 'A' completes a piece of work in 3 days, which 'B' completes it in 5 days and 'C' takes 10 days to complete the same work. How long will they take to complete the work , if they work together?
a. 1.5 days
b. 4.5 days
c. 7 days
d. 9.8 days
View solutionCorrect answer :(a)
Hint:
(A+ B+ C)'s one day work =  1  +  1  +  1  =  1 
3  5  10  1.5 
Hence, A ,B & C together will take 1.5 days to complete the work.