A) \[12{\scriptstyle{}^{1}/{}_{2}}\]days
B) \[13{\scriptstyle{}^{1}/{}_{2}}\] days
C) \[14{\scriptstyle{}^{1}/{}_{2}}\] days
D) \[17{\scriptstyle{}^{1}/{}_{2}}\] days
Correct Answer: A
Solution :
(a): Let 1 man do work in \['x;\] days Let 1 boy do work in 'y? days \[\Rightarrow 1\,man\to 1\,day\Rightarrow \frac{1}{x}work.\] \[\Rightarrow 1\text{ }boy\to 1\text{ }day\Rightarrow \frac{1}{y}work.\] \[\therefore \frac{1}{\frac{2}{x}+\frac{3}{y}}=10\] \[=\frac{2}{x}+\frac{3}{y}=\frac{1}{10}\] ??..I Similarly, \[\frac{3}{x}+\frac{2}{y}=\frac{1}{8}\] .....II \[I\times 3-II\times 2\] \[\Rightarrow \frac{9}{y}-\frac{4}{y}=\frac{3}{10}-\frac{2}{8}\] \[\Rightarrow \frac{5}{y}=\frac{24-20}{80}\] \[\Rightarrow y=\frac{400}{4}=100\]and hence, \[x=\frac{200}{7}\] \[\therefore \] 2 men, 1 boy can do work in \[\frac{1}{\frac{2}{x}+\frac{1}{y}}\]days \[=\frac{1}{\frac{7}{100}+\frac{1}{100}}\] \[=\frac{1}{\frac{8}{100}}=\frac{100}{8}\] \[=12\frac{1}{2}\] days
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