Important Short Tricks on Time and Work
Hello Friends,
Time and Work is a very easy topic and at least 3-4 Questions are asked
from this topic in SSC CGL, SSC
Aspirants and FCI Exam.What actually the Time and Work Topic is all about? In
simple words It's how much time a person will take to Complete a Given Work.
Here we are providing some cases of time and work and efficient method to
solve it. Hope this would be helpful to all aspirants.
Time : Time needed by more than one person to complete a job or time for
which a person(s) actually worked on the assigned job.
Work : The amount of total work or the part of total assigned work actually
done.
Note -: In conventional Method work is always treated as 1
Example: So if I say that a person can complete a work in 20 days that
means he will do 1/20 work in one day, It's simple maths.
Now another person does the same work in 30
days. So he will do 1/30 work in 1 day.
Now if i ask in how many days they will complete the work together
then is Add their 1 day of work
like (1/20 + 1/30) = (3+2)/60 = 5/60
= 1/12
Now this 1/12 we got is actually their 1 day work, So if they do 1/12 work
in one day then it's simple they will complete the whole work in 12 days.
Now that was the conventional method and I believe that you all know how to
solve Questions through Conventional method.
So now lets move on to the Faster
method i.e efficiency method.
In efficiency method the Work is not treated in numerical value, Like in
Conventional method the work is 1 but here the work is treated as percentage.
So by common sense the work is always treated as 100%
So when i say a person completes a work in 20 days it means he will do
100/20 % work in 1 day i.e 5 % work in 1 day
If another person does the work in 30 days that means he will do 3.33% work
in 1 day.
And together they will do 5 + 3.33 = 8.33 or 8.4% work in one day So in how
many days they will do the complete work, that will be 100/8.4 = 12 days.
Now it may sound difficult That we have to convert Each value in % but
don't worry you don't have to convert each value, You just have to learn all
the values till 1/60 and then it will be a cakewalk.
Now we will take Some standard Cases Of time and work and you all are free
to ask any problem if you have in any case.
Case 1 - A does a work in X days, B
does a Work in Y days In how many days they will complete the work.
Question- A completes the work in 6 days and B completes the work in 12
days In how many days they will complete the work.
Conventional Method :
Work done by A in 1 day = 1/6
Work Done by B in 1 day = 1/12
Work done By A & B together in 1 day = 1/6 + 1/12 = (2+1)/12 = 3/12 =
1/4
As A & B Completes 1/4 work in one day So they will complete the whole
work in 4 Days.
Efficiency method.
Efficiency of A =100/6 = 16.66%
Efficiency of B = 100/12 = 8.33%
Efficiency of A & B Together = 16.66+ 8.33 = 25%
So the time taken by A & B together to Complete the work will be 100/25
= 4 Days.
Case -2 : A can do a work in X days
and B can do it Y days, In how many days the work is completed if they work
alternatively Started by A.
Now in these type of question the person are not actually working together,
what happens in this type of question is that A works for 1 day and then on 2nd
day B work and on 3rd again A work and on Fourth again B works and so on till the
work is completed.
For example : A can do a work in 10 days B can do it 15 days and how many
days they will finish it if The work is started by A
So again work done by A in one day = 1/10
'' ''
'' '' ''
B '' ''
= 1/15
Now the work done by Together will be = 1/10 + 1/15 = 1/6 [ Note now this 1/6
work is not done by them in 1 day but in 2 days Actually, See A worked for 1
day and did 1/10 work on the second day B worked and finished the 1/15 work So
in total 2 days they did 1/6 work]
So in 2 days they did 1/6 work so in how many days they will complete the
whole work, Simple 12 days.
Efficiency Method :
A's Efficiency = 10%
B's Efficiency = 6.66%
A + B Efficiency = 16.66%
Work done by A and B in 2 days [ remember 2 days because they are not
working together but working alternatively] = 16.66%
So time taken by them to complete 100% work = 100/(16.66 = 6 [ but always
remember multiply this by 2, Because 16.66% work is done by them in 2 days and
not in 1 day.
So The answer will be 6*2 = 12 days.
Case 3: A can do a work in X days, B
can do the work Y days and A leaves after working Z days.
Question- A can do a work in 12 days and B can do it in 24 days, A works
for 3 days and then leaves, In how many days will the work be completed?
Now here we can so that A leaves after 3 days that means A and B only
worked for 3 days and the remaining work is done by B alone.
So first we have to calculated the work done by A and B together in 2 days.
So work done be A in 1 day = 1/12
"" " " "
B " " "
= 1/24
Work done by A & B together is 1 day = 1/12 + 1/24 = 1/8
Work done by A & B together in 2 days = (1/8) * 3 = 3/8
So remaining work = 1 - 3/8 = 5/8
Now this 5/8 work has to be done by B alone.
So it takes 24 days for B to do Complete work, How much time it will be
taken by B to do 5/8 work ? So it will be 24*(5/8) = 15 days
So the work will be completed in 3 + 15 days = 18 days
Efficiency method :
A's efficiency = 8.33 %
B's Efficiency = 4.16%
Total A+B = 12.49% = 12.50%
work done by A and B together in 2 days = 12.5*3 = 37.5 %
Work remaining = 62.5%
time taken by B to complete 62.5% work = 62.50/4.16 = 15 days
Total time = 15+3 = 18 days
Case 4 : A can do a piece of Work in
12 days and B can do it in 24 days, In how many days will the work be completed
if B leaves 2 days before the completion on work.
Now in this question B leaves before 2 days
Together they can do the work in what = 1/12 + 1/24 = 1/8
That means 8 Days.
That means Together they could have completed the work in 8 days but B
works only till 6th day and The remaining work will be done by A alone
So they worked together for 6 days in all So work done by them in 6 days =
(1/8)*6 = 3/4
remaining work = 1/4
Now this 1/4 work will be done by A alone
Now A can do the complete work in 12 days, So the time taken by him to do
1/4 work = 12 * (1/4) = 12/4 days or 3 days
So total time taken = 6+ 3 days = 9 days
Efficiency method :
A's efficiency = 8.33%
B's efficiency = 4.16%
Total = 12.49% = 12.5%
Work will be completed in 8 days
Work done in 6 days = 75%
remaining = 25%
A will complete the remaining in = 25/8.33 = 3
Total = 6+3 = 9 days
Case 5 :.If ‘M1’ persons can do ‘W1’
work in ‘D1’ days and ‘M2’ persons can do W2 work in D2, days then we have a
very general formula in the relationship of M1 D1 W2 = M2 D2 W1. The above
relationship can be taken as a very basic and all-in-one formula. We also
derive
A) More men less days and conversely more days less men.
B) More men more work and conversely more work more men.
C) More days more work and conversely more work more days.
Case 6 : If we include the working
hours (say T1 and T2) for the two groups then the relationship is
M1 D1 T1 W2 = M2 D2 T2 W1
Again, if the efficiency (Say E1 and E2) of the persons in two groups is
different then the relationship is
M1 D1 T1 E1 W2 = M2 D2 T2 E2 W1
Now, we should go ahead starting with simpler to difficult and more
difficult questions.
Note:- On the Basis of above short cut we will update quiz soon.
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