Latest Elitmus Aptitude Question SOLUTION: A, B and C working together completed a job in 10 days. However C only worked for the first three days when 37/100 of the job was done. Also, the work done by A in 5 days equals th

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(#M40039373) ELITMUS Numerical Ability question work and time Keep an EYE

A, B and C working together completed a job in 10 days. However C only worked for the first three days when 37/100 of the job was done. Also, the work done by A in 5 days equals the work done by B in 4 days. How many days will the fastest worker take to complete the given work alone?
20 days 25 days 30 days 40 days...........

Asked In Elitmus Aakash Jain (9 years ago)

Unsolved Read Solution (10)

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Kapil Dev Chauhan  (9 years ago)

A+B+C 3 day work = 37/100
remaining work= 63/100
A+B complete the work in 7 days= 9*7/100
A+B 1 day work= 9/100

Now A+B 1st 3 days work = 27 , remaining= 37-27=10
so in 1st 3 days A work = 10 , A 1 day work = 10/3
So, C alone needs 30 days to complete the work

A 5 day work = B 4 day work (Clearly B is more efficient than A)
A efficiency = 20%
B efficiency = 25%

Now A+B 1 day work = 9 {i.e A is doing 4/9 part and B is doing 5/9}
If A work alone = 25 Days
If B work alone = 20 Days

Is this solution Helpfull? Yes (16) | No (5)  

avinash jha  (9 years ago)

work done by a,b,c in 3 days = 37/100
work done by a+b in 7 days = 63/100
so, 1/a+1/b=63/7*100 and 5*a=4*b
By solving you get a=20 and b=25.
By substitution of a,b in 1/+1/b+1/c=37/100*3 we get c=7/25
so in 1 day a does 5%(1/20) work, b does 4%(1/25) work and c does 3.57% work
so a is fastest and require 20 days to complete the work alone

Is this solution Helpfull? Yes (14) | No (9)  

Bharti jain  (9 years ago)

work done by a,b,c in three days =37/100
remaining work done by a,b in 7 days =63/100
1 day work done by a+b=9/100
then 1 day work of c=1/100
after calculation
one day work of a=1/20
one day work of b=1/25
so A is the fastest worker done in 20 days...

Is this solution Helpfull? Yes (10) | No (11)  

veer kumar  (9 years ago)

i think there is a mistake in the question
as if (a+b+c) can complete the work in 10 days then
3 days work (a+b+c)=3/10------(1)
now its given that c's(alone) 3 days work is 37/100
and 37/100 is greater than 3/10 !!!!!!!!! thats not possible

Is this solution Helpfull? Yes (8) | No (5)  

Ayush Upadhyaya  (8 years ago)

Solution based on Efficiency
Since A+B+C completed 37% of the work working together in 3 days
so per day efficiency of A+B+C=37/3=12.33%
and A & B Completed the remaining work i.e. 63% in 7 days
so combined per day efficiency of A+B=9% ..............(1)
Since work done by A in 5 days= work done by B in 4 days
that means B is more efficient than A
now look towards options
lets say B Completes 100% work in 20 Days
so per day Efficiency of B=5%
from 1 we get
per day efficiency of A=4%
so days taken by A to complete 100% work=25 days
and also the work done by A in 5 days(5*4=20)=work done by B in 4 days(4*5=20)
hence B is the fastest worker and completes work in 20 days!!

Is this solution Helpfull? Yes (7) | No   

abhishek  (9 years ago)

arun sharma l2 18th q
3(a+b+c)=37%
7(a+b)=63%
a+b=9% work of one day after c leaving
and also 5A=4B
b=25%,a=20% devide this by 5 coz a takes 5
hence one day of work a=4%,b=5%
hence whole work can be done in 100%/5%=20 days

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

sunny kumar  (9 years ago)

IF A B,C COMPLETE=ING THE WORK IN 20,25,30 THEN A+B+C WON'T BE ABLE TO COMPLETE THE WORK IN 10 DAYS...

WRONG QUESTION

Is this solution Helpfull? Yes (3) | No (6)  

Anuj Gupta  (7 years ago)

1/a + 1/b + 1/c = 1/10 (Given)

3(1/a + 1/b + 1/c) = 37/100 (given)
and c lefts after this so,
1/a + 1/b = 63/100
5a = 4b (given)
solving these two equstions
a=20 and b= 25
now solving first equation c=100
so a is the fastest worker.

Is this solution Helpfull? Yes (1) | No   

CHANDRA SHEKHAR BHARDWAJ  (9 years ago)

It is right that answer can be 5E but here it can not be determined because how many times ratio becomes 16:9 is not given.

Is this solution Helpfull? Yes | No (1)  

Amit kumar  (2 years ago)

Let work is 1000
Work done by a+b in 7 days
(A+B)*7=63
One day work done by a+b=9
Iab+c in three day. 3(a+b+c)=37
But value of a+b will get c one day work. 10/3
5A=4B = equal work &. A+b. =9 from above
there for A one day work 4
And b one day work. 5
Total work done by. A=. 100/4=25 day
B=100/5=20 day. And
C=. 100/(10/3)=30 days
Hence fastest is B

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