Latest Elitmus Aptitude Question SOLUTION: A is a creater nd B is a destroyer. A can complete a building in 20 days while B can destroy it in 30 days. If both working alternate days,then after how much time will be the buil

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(#M40017890) ELITMUS Numerical Ability question Keep an EYE

A is a creater nd B is a destroyer. A can complete a building in 20 days while B can destroy it in 30 days. If both working alternate days,then after how much time will be the building completes for the first time?

Asked In Elitmus Mukesh Kr Singh (11 years ago)

Unsolved Read Solution (13)

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Prabhu  (11 years ago)

Ans)115 days

A 1 day=+1/20
B 1 day=-1/30
In 2 days building will be complete 1/20-1/30=1/60
so days are reqired=120...but
If full building work is 1, then before B destroy ,A complete the building .so
completed building work before A finished =>(1-1/20)=19/20 ,this will gives the number of pair A,B works...
consider x is number of pair days work of A,B...

1/60*x=19/20=>x=57;
so number of days=2 * pair days ;
number of days A and B work =114;
at last A done ramaining work, so 114+1=115
Ans)115 days

Is this solution Helpfull? Yes (57) | No (3)  

Aman  (11 years ago)

115

A's 1 day=+1/20
B's 1 day=-1/30
In 2 days building will be complete 1/20-1/30=1/60

(1-1/20 = ) 19/20 part of wall will be made in 114 days.
on 115th day balance 1/20 th will be made by creator.

Is this solution Helpfull? Yes (30) | No (4)  

sunny kumar  (9 years ago)

Let us say that the wall is of 60 bricks

A builds 3 bricks every day
B destroys 2 bricks every day

If A and B work on alternate days then 1 brick will be added every 2 days.

After 114 days, 57 bricks will be added. Now it will be turn of A to build 3 bricks. Hence on 115th day 60 bricks will be completed

Is this solution Helpfull? Yes (19) | No   

Vishnu Dutt Yadav  (11 years ago)

A's 1 day=+1/20
B's 1 day=-1/30
In 2 days building will be complete 1/20-1/30=1/60
2 days =1/60
=>2*60 days=1
i.e it require 120 days....

Is this solution Helpfull? Yes (10) | No (33)  

srinivasulareddy  (11 years ago)

in 2 days they complete building 1/60 part.so they both complete in 120 days

Is this solution Helpfull? Yes (4) | No (19)  

dharmendra  (11 years ago)

one day creation of the A is =1/20
one day destruction of the B is =1/30
so 2 day construction is=1/20-1/30=1/60
to complete work each take 60 turn
so days are reqired=120

Is this solution Helpfull? Yes (4) | No (18)  

SHUBHASIS CHANDA  (11 years ago)

a does 1/20 work in 1 day
b destroys 1/30 work in 1 day.
together they do 1/20-1/30 work in one day that is 1/60 work
hence they take 60 days to complete building

Is this solution Helpfull? Yes (3) | No (23)  

gaurav  (7 years ago)

Lets say total work to be done is LCM of 20&30 which is 60 UNIT.

A's work for 1 day is 60/20=3 UNIT.

B's work for one day is 60/30=2 UNIT but negative or -2 unit.

now here A starts first because B demolishes , or demolition only can be done if there is some work already done.
so here (A+B) will be a pair for two days work which yields 1 unit work in 2 days.
hence this will continue for 114 days which will yield 57 unit work but on the end of 115th day the works will be 60 unit or 100% hence the work will be first completed on 115th day.


HENCE answer is 115 day

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Jessica Olivia D'Souza  (10 years ago)

can anyone explain why the solution shouldn't stop at 120 days?

Is this solution Helpfull? Yes | No (4)  

Deepesh  (10 years ago)

Days Efficiency
A - 20(days) ----- 5% (100/20)
B - 30(days) ----- -3.33% (100/30)

Total efficiency in 2 days = 1.66

Building will be completed when eff =100;

( 100 / 1.66 )*2 = 120 days

Is this solution Helpfull? Yes | No (5)  

Vikash kumar  (7 years ago)

correct answer=120
short cut method:
days total unit
60
a=20 3
b=30 - 2
total one day work=1
here a start the work so pattern like ab ab ab......
so one pattern work=60
so 60/1=60 pattern
one pattern =2 days
so 60 pattern 2*60=120 days is the correct answer

total work 12

Is this solution Helpfull? Yes | No (2)  

Amit Kumar Singh  (7 years ago)

A one days work 1/20= 5%
B one day work 1/30 = -3.33%

2 day's work = 5-3.33= 1.68%

They work together until they complete the 95% work and final 5% would be done by A itself

1.68*x=95
x=114
now A will do the remaining 5% of work in last day it would be = 114+1= 115

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Roopesh kumar  (7 years ago)

let total unit of work is 60 unit
then A do 3 nit of work in 1 day and B do 2 unit of work in 1 day
resultant nit of work = 3-2=1 unit per day
it takes 57 days to complete 57 unit of work...... as next day A do 3 unit of work and it reaches 60 unit(total work)
hence total 57+1= 58 days required to complete the building for the first time :P

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