Latest elitmus Aptitude Question SOLUTION: a work is done by workers each day one worker get rmove and work get finished when all the workers remove.If they all together do the work then they take 0.6 of time taken by above

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(#M40152717) ELITMUS Numerical Ability question time and work Keep an EYE

a work is done by workers each day one worker get rmove and work get finished when all the workers remove.If they all together do the work then they take 0.6 of time taken by above procedure.find in how many days a single worker can complete a work

Asked In elitmus SAURABH GUPTA (8 years ago)

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Read Solution (6) :

Ajitesh rai  (8 years ago)

Suppose single worker can complete the work in 'x' days

Hence a workers one days work is 1/x

Suppose there are 'n' workers

Procedure 1---------
The work would be completed in 'n-1' days (as given in question)

Also,
First days work is = n/x
Second days work = (n-1) / x
third days work = (n-2) / x
n-1 days work is = 1/x

Adding all days work

n/x + n-1/x + n-2/x + 1/x = 1 { Standard equation }

Solving, we get
(1/x) * (n*(n+1)/2 ) =1

Hence , x = n(n+1)/2 ----------Equation 1-------


Procedure 2---------
(1/x + 1/x + 1/x + .............1/x) * d = 1 { Standard equation }
Total no of workers are 'n' and 'd' are the no of days , hence above equation becomes

(n/x) * d = 1

d = x/n days

According to question
Days in procedure 2 = .6 * days in procedure 1
Hence,
x/n = .6(n-1)

x==6n(n-1) / 10 ----------------equation 2---------

Solving equation 1 and 2..

We get n = 11 , and x = 66 ..

Hence Single worker complete works in 11 days ...(Ans)

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Aditya dhanuka  (8 years ago)

first procedure will complete in n days .
second procedure will complete in x/n days
according to question x/n=0.6n

x=0.6n^2..................................eq1


from given solution=n*(n+1)/2=x............................eq2
solving 1 and 2
n=5 and x =15days(answer)

Is this solution Helpfull? Yes (6) | No (1)  

Karna  (8 years ago)

@Ajitesh Rai, work is completing in n days not in n-1 days

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ananga  (8 years ago)

anyone?? other than this

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AKHIL KALRA  (8 years ago)

is it's answer is 55 days

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Shahroz Saleem  (7 years ago)

Suppose, there are 'm' no. of total workers. In the first scenario, the work lasts for 'm' no. of days.

w1+w2+w3+...+wm = W (total work)
wi representing work on each day.

m + m-1 + m-2 + ...... + 1 = W
m(m+1)/2 = W ....eqn-1

In second scenario,
m*0.6m = W ....eqn-2

Equating eqn-1 nd eqn-2
m = 10.

This means, in first scenario work was done in 10 days. So now in second scenario, this work will be done in 6 days.

now the question boils down to- A work is done by 10 men in 6 days then how many days will be taken by 1 man to do the same work.

1 * t = 10 * 6
t = 60 days.

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