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kashif2day: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Mon Jun 20, 2011 9:53 pm

by kashif2day » Tue Jun 28, 2011 4:18 am

the average salary per head of all workers in a factory is Rs60.the average salary per head of the officer is 400 and that of the rest is 56,if there are 12 officers,the total number of workers in the factory are? ans :1032 ,,can any one explain how?

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Source: Beat The GMAT — Problem Solving | Tue Jun 28, 2011 4:18 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue Jun 28, 2011 4:37 am

Hi,
workers = officers + rest
Let the number of workers be n
So, n*60 = 12*400 + (n-12)*56
=> n(60-56) = 12(400-56)
=> n*4 = 12*344.
So, n= 3*344 = 1032

Cheers!

Things are not what they appear to be... nor are they otherwise

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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 » Tue Jun 28, 2011 7:14 am

kashif2day wrote:the average salary per head of all workers in a factory is Rs60.the average salary per head of the officer is 400 and that of the rest is 56,if there are 12 officers,the total number of workers in the factory are?

Say the number of workers = W = (Number of officers + Rest)
Hence, Rest = (W - 12)

Total salary = (Total number of worker)*(Avg salary per head of all workers) = 60W

Again, total salary = Total salary of the officers + Total salary of the rest = 12*400 + (W - 12)*56

So, 60W = 12*400 + 56(W - 12)
--> 60W = 4800 + 56W - 12*56
--> 4W = 4800 - 12*56
--> W = (4800 - 12*56)/4 = 1200 - 3*56 = 1200 - 168 = 1032

Therefore, the total number of workers in the factory is 1032.

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Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Tue Jun 28, 2011 7:54 am

kashif2day wrote:the average salary per head of all workers in a factory is Rs60.the average salary per head of the officer is 400 and that of the rest is 56,if there are 12 officers,the total number of workers in the factory are? ans :1032 ,,can any one explain how?

Each officer is 340 above the average. Together, the 12 officers "contribute" 340*12 Rs above the average - a quantity that needs to be offset by an x number of workers, each of which is 4 below the average of 60. Thus, the number of workers needed to offset 340*12 is

x=340*12 / 4 = 340*3 = 1020.

So there are 12 officers at 400, and 1020 workers at 56, and together these two groups offset each other to an average of 60. total of 12+1020 = 1032 workers in the factory.

Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com

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