Latest Elitmus Aptitude Question SOLUTION: if a group of people start to do a work and each day one member of the group leaves. And when last person leaves work gets completed. If all members of the group does the work for

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(#M40030041) ELITMUS Logical Reasoning question elitmus quant 11/10/2013 Keep an EYE

if a group of people start to do a work and each day one member of the group leaves. And when last person leaves work gets completed. If all members of the group does the work for every day(no member leaves) then work gets completed in 0.6 times of what it takes when being done in the previous way(1 person leaving each day).So, we hv 2 find out if the work will be done by a single person then how many days it will take?

Asked In Elitmus Amardip Gautam (10 years ago)

Unsolved Read Solution (8)

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Read Solution (8) :

Mahesh  (10 years ago)

If the total number of people is n, everyday one person leaves and it takes n days to complete the work, so for example if there are 10 people it takes 10 days to complete the work and the total number of people worked is 10 + 9+ 8 .......+1

So, for n people it will be n+(n-1)+(n-2).....+1 = n(n+1)/2

In the second case the same n people worked for only 0.6 part of the initial time, as the initial time is n days, the second case they worked for 0.6 * n days.
So, total mandays in the second case, that is number of men and number of days is
n* (0.6 n)

As the work is the same in both the cases
n(n+1)/2 = n(0.6)n
n+1= 1.2 n
n=5

So, 5 is the answer
Initially 5 people started the work and every day one person left, so total mandays = 5+4+3+2+1 = 15
In the second case 5 people has to work for only three days to complete the work, as the total mandays needed is only 15.
Time became three days which is 0.6 times of the initial time that is 5 days.

Is this solution Helpfull? Yes (83) | No (3)  

kharak  (10 years ago)

let total no of people are 'n'.let one person complete work in 'x' days.
then time taken by 'n' person to complete work ll be 'x/n'.
and by another condition work ll complete using
1/x[n+(n-1)+(n-2)+......+1]=1
x=n(n+1)/2 and this way toal time to complete work is 'n'
as condition is given :x/n=.6n so x=.6*n^2
now doing both values of x equal we get n=5 and x=15

Is this solution Helpfull? Yes (8) | No (1)  

sravani  (9 years ago)

let the no.of people be n.
so,n+n-1+....+1=n(n+1)/2
given this equals 0.6n of previous day i.,e n*0.6n
n(0.6n)=n(n+1)/2
3/5 n^2 = n^2 +n / 2
n=5.
total days taken is 5(5+1)/2=15
s0,5---------15
as days and men are inversely proportional
1-------15*5=75 days.
single takes 75 days.

Is this solution Helpfull? Yes (1) | No (2)  

PRIYA SATSANGI  (10 years ago)

6days=6=5=4=3=2=1=21 men
21 days

Is this solution Helpfull? Yes | No (6)  

Jeevana  (10 years ago)

15 days
5persons-3days => 1person-15days

Is this solution Helpfull? Yes | No (2)  

SOURAV KUNWAR  (10 years ago)

Let 3 people r there each can do 10 unit work in a day.
let there is 60 unit work..
first day 30
2nd day 20 (1 worker left)
3rd day 10
30+20+10=60 work complete in 3 days
All workin together will take 60/30 = 2 days i.e 0.6 of 3 days..
so each worker can do the work in 60/10 = 6 days ..
Ans = 6 days..

Is this solution Helpfull? Yes | No (3)  

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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chandan kumar  (8 years ago)

suppose we have N person workes for X days when 1 person leaves each day
so if day don't leaves then no of days of work =0.6X
now,
N person work for 0.6X days for complete 1 work
so 1. . . . . . . . . . . . . . . 1 day . . . . . . . . . . . . 1/(0.6NX) work

now according to question

N(1/(0.6NX))+(N-1)/(1/(0.6NX))+......................+1/(1/(0.6NX))=1
=>N(N+1)/(1.2NX)=1
=>5(N+1)/(6X)=1

=> N=X=5

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