A) 8 minutes
B) 6 minutes
C) 10 minutes
D) 4 minutes
Correct Answer: A
Solution :
Let after x men B should be closed then, The part filled by (A + B) in x min. + the part filled by A in (18 - x) = 1 min. \[\therefore \,\,\,\,\,\,x\left( \frac{1}{24}+\frac{1}{32} \right)+(18-x)\times \frac{1}{24}=1\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{(32+24)x}{24\times 3224}+\frac{18-x}{24}=1\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{56x}{24\times 32}+\frac{18}{24}-\frac{x}{24}=1\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{7x}{96}-\frac{x}{24}=1-\frac{3}{4}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{7x-4x}{96}=\frac{1}{4}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3x=24\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=8\,\,\min \]
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