For work done problems,
If the problem involves two individuals, use this formula:
t=(m1*m2)/(m1+m2)
Here,
t= Total time taken if all individuals work together to complete the work.
m1= Time taken by the first individual to do the work alone.
m2= Time taken by the second individual to do the work alone.
Time & Work
Work is always considered as an entire value or one. There exists an analogy between the time-speed-distance 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) Number 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/xth) 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 that
a) 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's one day work = 1/x
B's one day work = 1/ y
(A + B)'s one day work = 1/x + 1/y
Together, they finish the work in xy/ (x+y) days.
b) If 'A', 'B' & 'C' can complete the work in x, y & z days respectively, then
(A + B+ C) 's 1 day work = 1/x + 1/y + 1/z = (xy + yz + xz) / xyz
Together, they complete the work in xyz / (xy + yz + xz) days.
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's one day work = 1/x
(A+B)'s one day work = 1/y
B's one day work = 1/y - 1/x = (x – y)/xy
So, 'B' alone will take xy/(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/x + 1/y + 1/z = 2(A+B+C)'s 1 one day work
Now, we have at hand (A + B + C)'s one day work = (1/x + 1/y + 1/z) / 2
(A+ B+ C) will together complete the work in 2/ (1/x + 1/y + 1/z) days
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/x - 1/y + 1/z) days = 2xyz / [xy + yz – zx] days
Similarly, - If B works alone, then time required = 2xyz / [- xy + yz + zx] days
- If C works alone, then time required = 2xyz / [xy - yz + zx] days
3) Man -Work -Hour related problems:
Remember that (M D H) / W is constant
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,
(M1 * T1) / W1 = (M2 * T2) / W2
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 (1/10th) part of the work.
FRAMEWORK:
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If the problem involves three individuals, use this formula:
t=(m1*m2*m3)/(m1m2+m2m3+m3m1)
Here,
t= Total time taken if all individuals work together to complete the work.
m1= Time taken by the first individual to do the work alone.
m2= Time taken by the second individual to do the work alone.
m3= Time taken by the third individual to do the work alone.
To know more about this topic, go to the link below:
Gmat Club - Work Rate Problems