Latest Elitmus Aptitude Question SOLUTION: If obama can complete a wall in 21 days and osama can destroy a wall in 28 days. Then how many days it would take to complete the work for the first time working in alternate days

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(#M40040369) ELITMUS Numerical Ability question Time and work Keep an EYE

If obama can complete a wall in 21 days and osama can destroy a wall in 28 days. Then how many days it would take to complete the work for the first time working in alternate days i.e, if obama works one day then second day in a week osama will work.????

Asked In Elitmus Aditya Kumar Singh (9 years ago)

Unsolved Read Solution (31)

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Read Solution (31) :

Sahil Choudhary  (9 years ago)

for making building obama will work one day more than osama.
so suppose osama works for n days
then obama will for n+1 days
and obama constructing rate=1/21 works per day
and osama destruction rate=1/28 works per day

so n*(1/21)-n*(1/28)+1/21=1
(n+1)*(1/21)-n*(1/28) = 1
4(n+1)-3n=84
n+4=84
n=80
so osama works for 80 days and obama works for 81 days
so 80+81=161
answer is 161

Is this solution Helpfull? Yes (51) | No (10)  

pankaj narayan  (9 years ago)

Work Done by Obama in 1 day = 1/21

Work DOne by Osama in 1 day = -1/28

Net work done by them in 2 days = 1/21 - 1/28 = 1/84

In one day = 1/168 .
Now Obama works last day 1/21 work

So remaining work = 20/21

Remaining work can be done in 20/21*168 = 160 days.

Total time required = 160 + 1 = 161 days.

Is this solution Helpfull? Yes (44) | No (3)  

Navpreet Singh  (9 years ago)

let the total work 84 lcm of 21 and 24.obama one day work 4 unit while osama 3 unit per day...
so net work per day 4-3(osama destroy)=1 unit
ths will take 2 day for 1 unit meaningfull work
we have to cmplete 84 unit
so 80unit take !80*2=160 days nd next day Obama do 4 unit so it wl take 161 total days

Is this solution Helpfull? Yes (17) | No (3)  

Faurabh Fuman  (9 years ago)

rate=work done/days work done=Lcm of 21 &28
obama(ob) 21 days 84/21=4 84
osama(os) 28 days 84/28=3
alternate work
ob os ob os......(ob=construct,os=destroy).
+4 -3 +4 -3
one unit of work is done in 2 days(4-3=1)
so that
last 2 days of work done by obama is
x+4=84;x is remaining work done
x=80;
80 work unit/1 unit per 2 days

80*2+1=161.

Is this solution Helpfull? Yes (8) | No   

Lakshminarayana  (9 years ago)

Total work is 168 days.
if we assume both are done the work 84units(lcm 21,28).a can do 4u/day.b can destroy 3u/day.both can do in 2 days as 1units. 84 units in 168 days

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GB  (9 years ago)

Answer = 168 days
Work done by Obama -> 1/21
negative work done by obama -> 1/28

total work done by them in 2 days -> 1/21-1/28 = 1/84

So 1 out of 84 parts of the work is done in 2 days
TIME ----------------------WORK DONE
2 days 1/84
? 1
= (1/2)/(1/84) = 2* 84= 168 days

Answer = 168 days

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aditya saraswat  (9 years ago)

161 days

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nirmala  (9 years ago)

1.LCM of 21 and 28 is 84
TW=84

2.obama 1 day complete work=4
osama 1 day destroy work =3
Total one day work =7

1day work completetion=4-3=1
first time only they will alternate so=2days,1work complete(1st day=4)-(2nd day=3)
83work complete both in 83d
83d+2d=85days to complete the work

Is this solution Helpfull? Yes (1) | No (4)  

SUPHALI ARORA  (9 years ago)

mine answer is 168. as one is making and other is destroying.. so together their 2 days work will be 1/21-//28=1/84... ie total work will be completed in 168 days..

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Nandan Kumar  (8 years ago)

ans =161 days

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kuldeep kumar  (8 years ago)

answer: 161 Days

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amit dhakad  (8 years ago)

ans is 161

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kumari snehlata  (7 years ago)

161 is the right ans.

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karan kishan  (6 years ago)

let obama starts the work.
Obama work of a day=100/21(in %)=4.76 %
Osama destroy a wall in a day=100/28(in %)=3.57%(1.19% less than obama's work)
Actually they are working alternatively,
therefore in 2 days the wall completed=1.19% ( of total construction.)
To acquire 100% of construction of the wall, days =(100-4.76)/(1.19/2) ->[1.19/2 means one day work %]
[Here, we need to subtract the one day work of Obama bcoz he will work one day more than Osama, i.e, 4.75%]
After solving, Days=95.24/0.595
or, Days=160.067(work completed in 161th days)

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rishabh  (9 years ago)

84 days and no
`

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Aditya Kumar Singh  (9 years ago)

Please explain @aditya saraswat how 161 days..

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DEEPAK SONI  (9 years ago)

As 1 day work121Bs 1 day work-128On 2nd day building will be complete 121-128184so no of days required will be168butIf full building work is 1 then before B destroy A complete the building so completed building work before A finished 1-1212021 this will gives the number of pair AB workslet x be the number of days work done by AB in pairsso we get 184x2021x80so number of days2 pair days number of days A and B work 160at last A done remaining work so 1601161

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Vishwanath sahu  (9 years ago)

2 days wok=1/21-1/28=1/84
soanswer is 83 days

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roopak  (9 years ago)

on 17 day wall will be completed

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Shivam Saluja  (9 years ago)

(1/21)-(1/28)=(1/x)
x= 21*28/7 = 28*3 = 84

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Ehtesham  (9 years ago)

let total work is 100;
obama in 21 days doea 100 work;
so in 1 day 100/21=4.76
now
osama in 28 days distroy 100 work;
so in 1 day 100/28=3.57;

now total work done in 2 day= 4.76 - 3.57(because its a negative work)
=1.19

now take 2 day work as 1 unit work;
so 1.19 work is done in 2 day
so ,100 work will be done in (2* 100)/1.19=168.06 days

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prashant raj  (9 years ago)

A/C TO QUESTION OBAMA WILL ONE DAY MORE THAN OSAMA
LET OSAMA WORKS FOR N DAYS THEN
N*1/21+1/21-N*1/28=1
N=80
N+1=81
SO TOTAL DAYS=80+81=161

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kaustubh salunke  (9 years ago)

161 dayz is the ans

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yashita  (9 years ago)

168 days to complete work

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Ehtesham  (9 years ago)

combined work of obama and osama in 2 day =4.75-3.57=1.19


1.19*80=95.2%of work
so in 160 days both completed 95.2% of work
then 161th day obama will work so net work done at the ned of 161th day=95.2+4.76=99.96% of work

now at the 162th day osama will work os net work done at the ned of 162th day=99.96-3.57=96.39% of work;
now at the 163th day Obama will work,so at the end of 163th day

net work done=96.36+4.76=101.15

so 163th day work will be completed.

Ans:163

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RINJU ELGIN  (9 years ago)

WORK=EFFICIENCY * TIME
OBAMA=21
OSAMA=28
LCM(TOTAL WORK)=84
EFF OF OBAMA=4
EFF OF OSAMA=3
FIRST DAY OBAMA COMPLETE 4
2ND DAY OSAMA COMPLETE 3
TOTAL 2 DAYS THEY COMPLETE 7 WORK
2*12 DAY THEY COMPLETE 7*12 WORKS
IE,24 DAY REQUIRED TO COMPLETE THE WORK

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sandhya ambatii  (8 years ago)

obama 1day wrk=1/21
osama 1 day wrk=1/28
total wrk for 2 days=1/21-1/28=1/84
so total work cmplted in 168 days

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Vikash kumar  (7 years ago)

correct answer is 168 days

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Ashishkumar Satappa Bhosale  (7 years ago)

At the last day of construction of wall, obama will do 1/21 of work and complete the wall.
so remaining work is 1- 1/20 = 20/21.

if both work together but ate alternate day...so 1/21 - 1/28 = 1/84 (this is 2 day work)
so one day work = 1/168

so no days of construction is (20/21) / (1/184) + 1 = 161

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rajat bhawsar  (7 years ago)

ans is 161 days

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Amritesh Anand  (6 years ago)

Ans is 161 days

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