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gmat7202011: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Sat Dec 11, 2010 2:39 pm; Thanked: 3 times

by gmat7202011 » Sat Feb 05, 2011 10:37 am

Ashok and Mohan can do a piece of work in 12 days
Mohan and Binod and do the same work in 15 days

If Ashok is twice as good a workman as Binod is, In how much time will Mohan complete the work alone

Thank You

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Source: Beat The GMAT — Problem Solving | Sat Feb 05, 2011 10:37 am

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sat Feb 05, 2011 11:29 am

gmat7202011 wrote:Ashok and Mohan can do a piece of work in 12 days
Mohan and Binod and do the same work in 15 days

If Ashok is twice as good a workman as Binod is, In how much time will Mohan complete the work alone

Thank You

A+M=1/12
M+B=1/15
A=2B; M-?

A=1/12-M; B=A/2; M+(1/12-M)/2=1/15 --> 30M+15/12-15M=2 --> 15M=9/12 --> M=9/(12*15)=1/20

Mohan will complete work in 20 days alone

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Feb 05, 2011 10:35 pm

gmat7202011 wrote:Ashok and Mohan can do a piece of work in 12 days
Mohan and Binod and do the same work in 15 days

If Ashok is twice as good a workman as Binod is, In how much time will Mohan complete the work alone

In one day, Ashok's work = 2*(Binod's work)
In one day, Ashok and Mohan can do 1/12 of the whole work, i.e. 2*(Binod) and Mohan can do 1/12 of the whole work. ...... (i)

In one day, Binod and Mohan can do 1/15 of the whole world. ....... (ii)

Subtracting (ii) from (i),

In one day, Binod can do (1/12 - 1/15) = 1/60 of the work ....... (iii)

Subtracting (iii) from (ii),

In one day, Mohan can do (1/15 - 1/60) = 3/60 = 1/20 of the whole work

Therefore, Mohan will complete the work in 20 days.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Feb 06, 2011 3:47 am

gmat7202011 wrote:Ashok and Mohan can do a piece of work in 12 days
Mohan and Binod and do the same work in 15 days

If Ashok is twice as good a workman as Binod is, In how much time will Mohan complete the work alone

Thank You

Plug in work = 60.
Combined rate for A+M = work/time = 60/12 = 5 units per day.
Combined rate for M+B = work/time = 60/15 = 4 units per day.
Subtracting, we get (A+M) - (M+B) = A-B = 5-4 = 1 unit per day.

Since A's work is twice as good, A=2B.
Substituting A=2B into A-B = 1, we get:
2B-B = 1.
B=1.

Substituting B=1 into M+B = 4 units per day, we get:
M+1 = 4.
M = 3 units per day.
Time for M = work/rate = 60/3 = 20 days.

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