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Archit3110
Major Poster
27 Jun 2020, 08:25
Kudos
Bookmarks
Rate of Tom ; 1/6 ; Rate of Peter ; 1/3 and Rate of Tom ; 1/2
first 1 hour ; Tom did 1/6th of work left with 5x/6 of work
2nd hour Rt + R P ( 1/6+1/3) ; 3/6 ; 1/2 ; work left ; 5x/6-x/2 ; x/3
3rd hour Rt+Rp+R J ; (1/6+1/3+1/2) ; 1 ; work done ; x/3
total work done by Peter ; first hour he did 1/3 and in 2nd hour Peter did 1/3rd of x/3 work
total work done by Peter ; 1/3+1/3*1/3 ; 1/3+1/9 ; 4/9
OPTION E
first 1 hour ; Tom did 1/6th of work left with 5x/6 of work
2nd hour Rt + R P ( 1/6+1/3) ; 3/6 ; 1/2 ; work left ; 5x/6-x/2 ; x/3
3rd hour Rt+Rp+R J ; (1/6+1/3+1/2) ; 1 ; work done ; x/3
total work done by Peter ; first hour he did 1/3 and in 2nd hour Peter did 1/3rd of x/3 work
total work done by Peter ; 1/3+1/3*1/3 ; 1/3+1/9 ; 4/9
OPTION E
docabuzar
29 Jun 2020, 06:44
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docabuzar
let, total work = LCM of 6,3,2
=6
Tom one hour work= \(\frac{6}{6}\) =1
Peter one hour work=\(\frac{6}{3}\) =2
John one hour work =\(\frac{6}{2}\) =3
Tom work of 1 hr = 1
Tom and Peter work for 1 hr = 1+2=3
now, the total amount of work left = 6-4=2
if all 3 work for an hour= 1+2+3=6
but we require 2 unit of work, so divide the whole by 3
total work in last t hour= \(\frac{1}{3}\)+\(\frac{2}{3}\)+\(\frac{3}{3}\) = 2
total work done by peter = 2+ \(\frac{2}{3}\)= \(\frac{8}{3}\)
the fraction of work done by peter=(8/3)/6= \(\frac{4}{9}\)
IMO is E
30 Jul 2023, 12:49
Kudos
Bookmarks
Tom's rate = 1/6
Peter's = 1/3
John's = 1/2
Amount of work Tom does alone in one hour = 1/6
Peter and Tom in one hour will do 1/6 + 1/3 = 1/2
Total amount of work done = 1/6 + 1/2 = 2/3
So amount of work left undone = 1/3.
So time taken for the three of them to do the remaining work =
Let time needed for that be x.
1/6 + 1/3 + 1/2 = 1/3x
Which will give x = 1/3hours.
Therefore, fraction of work done by Peter,
First one hour
1/3
Work done for 1/3 hour
= 1/9
Total
1/3 + 1/9 = 4/9
GMAT quant instructor Lagos Nigeria.
Posted from my mobile device
Peter's = 1/3
John's = 1/2
Amount of work Tom does alone in one hour = 1/6
Peter and Tom in one hour will do 1/6 + 1/3 = 1/2
Total amount of work done = 1/6 + 1/2 = 2/3
So amount of work left undone = 1/3.
So time taken for the three of them to do the remaining work =
Let time needed for that be x.
1/6 + 1/3 + 1/2 = 1/3x
Which will give x = 1/3hours.
Therefore, fraction of work done by Peter,
First one hour
1/3
Work done for 1/3 hour
= 1/9
Total
1/3 + 1/9 = 4/9
GMAT quant instructor Lagos Nigeria.
Posted from my mobile device
