Question Number 40300 by mondodotto@gmail.com last updated on 18/Jul/18
$$\mathrm{10}\:\boldsymbol{\mathrm{men}}\:\boldsymbol{\mathrm{had}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{work}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{cultivating}} \\ $$$$\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{farm}}\:\boldsymbol{\mathrm{for}}\:\mathrm{18}\:\boldsymbol{\mathrm{days}}.\:\boldsymbol{\mathrm{when}}\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{work}}\:\boldsymbol{\mathrm{was}}\:\boldsymbol{\mathrm{done}}\:\mathrm{6}\:\boldsymbol{\mathrm{men}}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{reduced}}. \\ $$$$\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{long}}\:\boldsymbol{\mathrm{was}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{work}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{cultivating}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{farm}}\:\boldsymbol{\mathrm{done}}? \\ $$
Answered by MJS last updated on 18/Jul/18
$$\mathrm{the}\:\mathrm{work}\:={w} \\ $$$${w}=\mathrm{10}{m}×\mathrm{18}{d}=\mathrm{180}{md} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}{w}=\mathrm{60}{md}\:\Rightarrow\:\mathrm{10}\:\mathrm{men}\:\mathrm{worked}\:\mathrm{6}\:\mathrm{days} \\ $$$$\mathrm{180}{md}−\mathrm{60}{md}=\mathrm{120}{md}\:\mathrm{is}\:\mathrm{left} \\ $$$$\mathrm{4}{m}×{xd}=\mathrm{120}{md}\:\Rightarrow\:{x}=\mathrm{30}\:\Rightarrow\:\mathrm{4}\:\mathrm{men}\:\mathrm{worked}\:\mathrm{30}\:\mathrm{days} \\ $$$$\mathrm{the}\:\mathrm{work}\:\mathrm{was}\:\mathrm{done}\:\mathrm{within}\:\mathrm{36}\:\mathrm{days} \\ $$
Commented by mondodotto@gmail.com last updated on 18/Jul/18
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much} \\ $$