\(8w=6m=12b\)

or, \(4w=3m=6b\)

\(12m+12w+12b=12m+12(\frac{3}{4})m+12(\frac{3}{6})m=27m\)

Let x be the number of days to complete the work;

\(27*8*x=9*6*6\)

\(x=\frac{3}{2}\)

Ans A

meanup May I ask where the "8" comes from in the last expression? Thank you!

The question is missing one figure. Actually, the question should be as follows:

The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours. If working 6 hours per day 9 men can complete a work in 6 days, then in how many days can 12 men, 12 women and 12 boys together finish the same working 8 hours per day?

Hope this will help

Thanks! I assumed 6 hours in 2nd scenario as well because time was not mentioned and I was getting 2 days as the answer which was not available in the options

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I was making mistake of forming equation 8w= 6m+ 12b.
Could some one help to let me understand error in interpretation of question stem

given the description in the question,
"The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and the work done by a boy in 12 hours."
assume one woman 8 hrs = one man 6 hrs = one boy 12 hrs = x

scenario (1): "working 6 hours per day" 9 men can complete a work in 6 days = 6*9x =54x

scenario (2): "12 men, 12 women and 12 boys together finish the same work working 8 hours per day"
do the conversion
12 men 8 hrs = 16 man 6 hrs = 16x
12 women 8 hrs = 12x
12 boys 8 hrs = 8 boys 12 hrs = 8x
add up each of them, 16x+12x+8x=36x

if in scenario(1), the volume of task "working 6 hours per day 9 men(9X) can complete a work in 6 days"= 54x,
then how many days we need to complete the task in scenario(2) = 36x ?

9x * 6 days = 36x * ? days

54x / 36x = 3 / 2 days, ans(A)