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Bunuel
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meanup
\((3m+12w)*8=(2m+4w)*15\)

\(24m+96w=30m+60w\)

\(30m-24m=96w-60w\)

\(6m=36w\)

\(\frac{m}{w} = \frac{36}{6}=\frac{6}{1}\)

The efficiency of \(m=6\) and \(w=1\)

Substitute the value of \(m\) and \(w\) in any of the above equation to find the total work.

Total Work \(= (3*6+12*1)*8=(18+12)*8=240\)

This work is completed by \(10w \), Therefore, efficiency of \(10w= 10*1=10\)

Time taken \(=\frac{240}{10}=24\)

Ans C



Your solution doesnt hold right if you take the second equation into consideration, i.e. (2M+8W)*15= (2*6+8*1)15= 300.

the question should have been a little fair to not to choose between 24 or 30.
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VeritasKarishma Bunuel

would you like to hop in and answer for us?
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meanup
\((3m+12w)*8=(2m+4w)*15\)

\(24m+96w=30m+60w\)

\(30m-24m=96w-60w\)

\(6m=36w\)

\(\frac{m}{w} = \frac{36}{6}=\frac{6}{1}\)

The efficiency of \(m=6\) and \(w=1\)

Substitute the value of \(m\) and \(w\) in any of the above equation to find the total work.

Total Work \(= (3*6+12*1)*8=(18+12)*8=240\)

This work is completed by \(10w \), Therefore, efficiency of \(10w= 10*1=10\)

Time taken \(=\frac{240}{10}=24\)

Ans C



Your solution doesnt hold right if you take the second equation into consideration, i.e. (2M+8W)*15= (2*6+8*1)15= 300. "This is not the second equation, the second equation is \((2m+4w)*15\)"

the question should have been a little fair to not to choose between 24 or 30.

The second equation is (2*6+4*1)*15=(12+4)*15=16*15=240

So the method is correct😂 and has only one solution.

Posted from my mobile device
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Dear Bunuel

The answer is 24 (i.e. Ans C). Could you please verify it.
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meanup
Dear Bunuel

The answer is 24 (i.e. Ans C). Could you please verify it.
____________________
Fixed the OA. Thank you!
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Bunuel
3 men & 12 women finish a job in 8 days while 2 men and 4 women finish it in 15 days. In how many days will 10 women working together will finish the same job?

(A) 15
(B) 20
(C) 24
(D) 30
(E) 32

There are some great solutions already posted. But let's say you don't spot a solution like one of those and/or you just feel stuck. If that happens, always see if you can figure anything out from the answer choices. Let's just test one or two. I like starting with B and D. Those also look like the two easiest numbers with which to work; awesome.

Let's try B.
It takes 10 women 20 days to complete the job. Let's make the job solving 200 GMAT questions. That means each woman solves 1 question per day.
2 men and 4 women take 15 days to finish 200 questions. The women solve a total of 60. That leaves 140, so each man solves 70 over the 15 days. Each man solves 4.667 per day.
3 men and 12 women solve 3(4.667)+12 = 26 per day. They work for 8 days. 8*26=208. That's too many. B is wrong.

Let's try D.
It takes 10 women 30 days to complete the job. Let's change the job to solving 300 GMAT questions. That means each woman solves 1 question per day.
2 men and 4 women take 15 days to finish 300 questions. The women solve a total of 60. That leaves 240, so each man solves 120 over the 15 days. Each man solves 8 per day.
3 men and 12 women solve 3(8)+12 = 36 per day. They work for 8 days. 8*36=288. That's not enough. D is wrong.

B was too many. D was not enough. We need something between.

Answer choice C.
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