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paint 9 homes in 96 hours?????????

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paint 9 homes in 96 hours?????????

by bhumika.k.shah » Thu Apr 01, 2010 12:07 pm
Eight workers from Company A can paint 7 homes in 84 hours. Working together, three workers from Company A and five workers from company B can paint 9 homes in 96 hours. If each worker from company A works at one constant rate, each worker from Company B works at another constant rate, and the amount of time required to paint each home is the same, how many workers from Company B are required to 9 paint homes in 60 hours?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

Source KNEWTON CAT

Detailed explanation as i am really bad @ this topic :( + difficulty level.
Last edited by bhumika.k.shah on Fri Apr 02, 2010 9:17 am, edited 1 time in total.
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by kevincanspain » Thu Apr 01, 2010 4:38 pm
The 8 workers from A can paint 1/12 of a home in 1 hour. Thus each worker A can paint 1/96 of a home in 1 hour

3 from A and 5 from B can paint 9/96 of a home in 1 hour- Since the 3 A's together paint 3/96 per hour, the 5 from B paint 6/96 of a home in 1 hour, or 1/80 each per hour.

In 60 hours, x B workers paint 60x/80= 3x/4 homes
Solving 3x/4= 9 for x, we get x=4(9)/3 =12 hours

Edited once I saw that the question had been incorrectly typed!
Last edited by kevincanspain on Fri Apr 02, 2010 1:32 pm, edited 1 time in total.
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by harshavardhanc » Fri Apr 02, 2010 4:15 am
kevincanspain wrote:The 8 workers from A can paint 1/12 of a home in 1 hour. Thus each worker A can paint 1/96 of a home in 1 hour

3 from A and 5 from B can paint 9/96 of a home in 1 hour- Since the 3 A's together paint 3/96 per hour, the 5 from B paint 6/96 of a home in 1 hour, or 1/80 each per hour.

In 96 hours, x B workers would paint 96x/80 =6x/5

Solving 6x/5 = 9 for x, we get x=5(9)/6 =7.5 hours

Alternatively, the 8 workers from A paint a home every 12 hours and thus would need 84 +12 =96 hours to paint 8 homes..Yet if 5 company A workers are replaced with 5 company B workers, 96 hours would be enough time to paint 9 homes, suggesting that company B workers are faster than their counterparts in A. This leads us to the conclusion that 8 company B workers would paint more than 9 homes in 96 hours--the answer should be less than 8!


Something is wrong here!
second your thoughts!

My approach :

find equivalence between type A and type B.

Step 1 : Find the number of A-workers who can paint 9 homes in 96 hours. It will be :

(84*8)/7 =(96*X)/9 => X= 9

Hence, 9 type-A ( 3+6) workers can paint 9 homes in 96 hours.

Now, as per the question :

3 type-A + 5 type-B can paint 9 homes in 96 hours.

or 5 type B workers are equal to 6 type-A . Hence, 9 type-A are equivalent to 3*2.5 = 7.5 type-B workers.

Ans= 7.5 :)
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by bhumika.k.shah » Fri Apr 02, 2010 4:43 am
Please check the OA and OE and then explain it to me :D
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by suryapal » Fri Apr 02, 2010 5:25 am
Eight workers from Company A can paint 7 homes in 84 hours. Working together, three workers from Company A and five workers from company B can paint 9 homes in 96 hours. If each worker from company A works at one constant rate, each worker from Company B works at another constant rate, and the amount of time required to paint each home is the same, how many workers from Company B are required to 9 paint homes in 60 hours?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
sol : given :--> 8 workers from company A can paint 7 homes in 84 hours or it can be represented as follows

8A ------>7H -------->84
so 8A------->1H---------> 84/7
AND 1A------->1H -------> 84*8/7

NOW 3A------>1H-------->(84*8)/(7*3)
AND 3A------>9H --------> (84*8*9)/(7*3) = 32*9 = 288

NOW given that three workers from Company A and five workers from company B can paint 9 homes in 96 hours and it can be written as ( according to formula)

(1/288) +(1/5B) = (1/96)
or (1/5B) = (1/96) - (1/288)
OR (1/5B) = (3-1)/288
OR 5B= 288/2 = 144

5 worker can completes a task in t hours then on worker complet it in (t*5) hours
so 1B---->9H ----> (144*5)

now the condition is one worker from company B paints 9 houses in (144/5) hours . then how many workers from company can paints 9 houses in 60 hours or it can be written as
xB ----> 9H -----> 60

by above two condition
(144*5)/x = 60
or x = 144*5/60 = 12

hence the answer is A

can anybody tell me the shorter way ...
Last edited by suryapal on Fri Apr 02, 2010 5:56 am, edited 2 times in total.
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by harshavardhanc » Fri Apr 02, 2010 5:50 am
bhumika.k.shah wrote:Please check the OA and OE and then explain it to me :D
Bhumika,

I know many members have made a mistake of posting a wrong question before, and this one comes in that same list!!!!

I'm a little annoyed that I and many others have spent our time in solving a question which had a mistake!

Anyway, I love Maths so much that i will try to forget this.

Your version asks for

how many workers from Company B are required to 9 paint homes in 96 hours?
whereas the original question asks for type B workers to paint 9 homes in 60 hours !!!!!!!

An advice to you :

Don't type the question. You have copy -paste options given by Mr. Gates. Use them.
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by harshavardhanc » Sat Apr 03, 2010 1:46 am
harshavardhanc wrote:
Hence, 9 type-A are equivalent to 3*2.5 = 7.5 type-B workers.

Ans= 7.5 :)
this was the answer had it been 96 hrs.

As the original one asks for 60 hrs . i.e 36/96 less or 3/8th less or 96 becomes 5/8th of itself,
therefore,
number of workers,calculated above(7.5), has to increase by 3/5 or becomes 8/5th of 7.5 = 12. :)
Regards,
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