Latest Elitmus Aptitude Question SOLUTION: a is 50% as efficient as b . c does half of the work done by a and b togetherif c alone does the work in 20 days,then a,b and c together can do the work in how many days?

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(#M40164077) ELITMUS Numerical Ability question Keep an EYE

a is 50% as efficient as b . c does half of the work done by a and b togetherif c alone does the work in 20 days,then a,b and c together can do the work in how many days?

Asked In Elitmus Sniper (7 years ago)

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Devendra Marghade  (7 years ago)

6 2/3 days

Let a,b and c can complete the work in A, B and C days respectively, then
I) a is 50% as efficient as b, so a requires twice the days required by b => A=2B ---(i)
II) c does half of the work done by a and b together => 1/C = (1/2)(1/A + 1/B) ---(ii)
III) 1/C=1/20 ---(iii)
Comparing (ii) & (iii), 1/20=(1/2)(1/A + 1/B) => 1/A + 1/B =1/10 ---(iv)
Substituting A=2B from (i) in (iv), we get 1/2B + 1/B= 1/10 => 1/B=1/15, so 1/A= 1/30
1 days work of a, b, & c = 1/A + 1/B + 1/C = 1/30 + 1/15 + 1/20 = 9/60= 3/20
Hence required days = 20/3 = 6 2/3

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karan kishan  (6 years ago)

try to use percentage concept to solve this kind of problem.
Now, See the solution:
C completes a work in 20 days who is half efficient of A and B together i.e, A and B finishes that work together in 10 days.
Now C work of a day=5%
A and B works of a day=10%
So A, B and C works of a day=5+10=15%
To acquire 100%(for work completion), Days=100/15=6*2/3 days.

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ManikumarSoruvu  (6 years ago)

given,
a is 150% efficicient than b
therefore Efficiency ratio of a:b=150:100 =>3:2
Ratio of time taken by a and b is=2:3
let a ,b,c takes x,y,z days respectievely to complete the work
1 day work of a &b=1/x + 1/y
therefore, 1 day work of c=(1/x +1/y)/2=1/z
=>1/20=(1/x+1/y)/2 ( c's 1 day work =1/20)
=>1/x + 1/y =1/10
now, 1 day work of a,b and c =1/10 +1/20 =3/20
therefore a ,b and c can complete the work in 20/3 days.

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Harshit Gupta  (6 years ago)

Let
A's one day work = 3
Then, B's one day work will be = 2 days (Since B is 50% more efficient than A )
C does half the work done by A and B, So
C's one day work = (3+2)/2
Therefore,
Work Ratio of 1 day for A, B and C is = 3 : 2 : 5/2
On Simplification Ratio becomes = 6 : 4 : 5
Therefore,
C completes the work in 20 days so
Total work = 5*20 = 100
A, B and C can together do the work in = 100 / (6 + 4+ 5)= 20/3 days

Ans. 20/3 days

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Ashishkumar Satappa Bhosale  (7 years ago)

Ans is correct = 6 2/3 , but Mr. Devendra said that , a and b are in ratio 2:1 , NO
a is 150% of b so ther are in ratio 3:2 .

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rajat bhawsar  (7 years ago)

ans is 20/3

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AISHWARYA MAHANA  (6 years ago)

let b=> x part
a=> 2x part
if we take the L.C.M. ,total they done 2x part
b-> x | 1day-2part
a->2x| 1day-1part
total in 1day they do(2+1=3part)
3part->1day
1part->1/3day
2xpart->2x/3days

according to question c does half of work and complete that task in 20 days
so time taken by c is, 2*2x/3=4x/3;
4x/3=20
x=15(time taken by b to complete task)
2x=30(time taken by a to complete task)

a=30|1day-4part
b=15|1day-8part
c=20|1day-6part
lcm=120
(4+8+6=18part)
18part-1day
120part-120/18=20/3

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  (6 years ago)

Let the whole work is =100%
c does 100% work in 20 days.
C's 1 day work=100/20=>5
According to question C is doing half the work done by A & B together; doesn’t it means that A + B together do 2*c one day work=5*2=>10
(A+B+C) one day work is 15
100% work done by (A+B+C)=100/15=>6.666

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prashant singh kushwaha  (5 years ago)

6 days 18 hr

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