A) \[1\frac{1}{2}\]days
B) \[3\]days
C) \[3\frac{2}{3}\]days
D) \[1\frac{1}{3}\]days
Correct Answer: A
Solution :
Work done per hour by a woman, a man and a boy x, y and z respectively. |
So, \[8x=6y=12z\] |
\[\Rightarrow \] \[x=\frac{3}{4}\,\,y\]and \[z=\frac{y}{2}\] |
9 men can complete a work in 6 days working 6 h/day |
\[\therefore \] Work done\[=9\times 6\times 6y=324y\] |
Work done by 12 men, 12 women and 12 boys in 1 day's working = 8 h/day |
\[=(12y+12x+12z)\times 8\] |
\[=\left[ 12y+12\times \frac{3}{4}y+12\times \frac{y}{2} \right]\times 8=216\,\,y\] |
Days required to finish work \[=\frac{324\,\,y}{216\,\,y}=1\frac{1}{2}\]days |
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