Question Number 33479 by mondodotto@gmail.com last updated on 17/Apr/18
$$\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{man}}\:\boldsymbol{\mathrm{takes}}\:\mathrm{15}\boldsymbol{\mathrm{days}}\:\boldsymbol{\mathrm{to}} \\ $$$$\boldsymbol{\mathrm{dig}}\:\mathrm{6}\:\boldsymbol{\mathrm{hectres}}.\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{long}}\:\boldsymbol{\mathrm{would}} \\ $$$$\mathrm{10}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{take}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{dig}}\:\mathrm{81}\:\boldsymbol{\mathrm{hectres}} \\ $$$$\boldsymbol{\mathrm{if}}\:\mathrm{2}\:\boldsymbol{\mathrm{boys}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{same}}\:\boldsymbol{\mathrm{amount}}\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{work}}\:\boldsymbol{\mathrm{as}}\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{man}}? \\ $$
Commented by MJS last updated on 17/Apr/18
$$\mathrm{1man}\:\:\mathrm{15days}\:\:\mathrm{6hectres} \\ $$$$\mathrm{1man}\:\:\frac{\mathrm{15}}{\mathrm{6}}=\frac{\mathrm{5}}{\mathrm{2}}\mathrm{days}\:\:\mathrm{1hectre} \\ $$$$\mathrm{1man}\:\:\mathrm{81}×\frac{\mathrm{5}}{\mathrm{2}}=\frac{\mathrm{405}}{\mathrm{2}}\mathrm{days}\:\:\mathrm{81hectres} \\ $$$$\mathrm{1boy}\:\:\mathrm{2}×\frac{\mathrm{405}}{\mathrm{2}}=\mathrm{405days}\:\:\mathrm{81hectres} \\ $$$$\mathrm{10boys}\:\:\frac{\mathrm{405}}{\mathrm{10}}=\mathrm{40}.\mathrm{5days}\:\:\mathrm{81hectres} \\ $$$$\mathrm{what}\:\mathrm{we}\:\mathrm{have}\:\mathrm{done}: \\ $$$$\left(\left(\left(\mathrm{15}/\mathrm{6}\right)×\mathrm{81}\right)×\mathrm{2}\right)/\mathrm{10}=\frac{\mathrm{15}×\mathrm{81}×\mathrm{2}}{\mathrm{6}×\mathrm{10}} \\ $$
Commented by mondodotto@gmail.com last updated on 17/Apr/18
$$\mathrm{still}\:\mathrm{i}\:\mathrm{don}'\mathrm{t}\:\mathrm{understand}\:\mathrm{this} \\ $$
Answered by Rasheed.Sindhi last updated on 17/Apr/18
$$\mathrm{10}\:\mathrm{boys}=\mathrm{5}\:\mathrm{men} \\ $$$$\begin{pmatrix}{\mathrm{men}}&{\mathrm{days}}&{\mathrm{hectres}}\\{\:\:\:\mathrm{1}}&{\:\:\mathrm{15}}&{\:\:\:\:\:\mathrm{6}}\\{\:\:\:\mathrm{5}}&{\:\:\:\mathrm{x}}&{\:\:\:\:\mathrm{81}}\\{\left(\mathrm{inverse}\right)}&{}&{\left(\mathrm{direct}\right)}\end{pmatrix} \\ $$$$\mathrm{x}:\mathrm{15}::\begin{cases}{\mathrm{1}:\mathrm{5}}\\{\mathrm{81}:\mathrm{6}}\end{cases} \\ $$$$\mathrm{x}×\mathrm{5}×\mathrm{6}=\mathrm{15}×\mathrm{1}×\mathrm{81} \\ $$$$\mathrm{x}=\frac{\mathrm{15}×\mathrm{1}×\mathrm{81}}{\mathrm{5}×\mathrm{6}}=\mathrm{40}\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{days} \\ $$
Commented by mondodotto@gmail.com last updated on 17/Apr/18
$$\mathrm{inverse}\:\&\:\mathrm{direct}\:\mathrm{what}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{sir}? \\ $$
Commented by Rasheed.Sindhi last updated on 17/Apr/18
$$\mathrm{Inverse}\:\mathrm{proportion}\:\&\:\mathrm{direct}\:\mathrm{proportion}. \\ $$
Answered by ajfour last updated on 17/Apr/18
$$\mathrm{2}{boys}\:\:\rightarrow\:\:\:\mathrm{6}{hectares}\:\:\:\rightarrow\:\:\:\mathrm{15}{days} \\ $$$$\mathrm{2}{boys}\:\:\rightarrow\:\:\:\mathrm{81}{hectares}\:\:\rightarrow\:\:\frac{\mathrm{15}}{\mathrm{6}}×\mathrm{81}{days} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{15}×\mathrm{27}}{\mathrm{2}}\:=\frac{\mathrm{405}}{\mathrm{2}}\:=\:\mathrm{202}\frac{\mathrm{1}}{\mathrm{2}}\:{days}\: \\ $$$$\mathrm{10}{boys}\:\:\rightarrow\:\:\:\mathrm{81}{hectares}\:\:\rightarrow\:\frac{\mathrm{405}}{\mathrm{2}}×\frac{\mathrm{2}}{\mathrm{10}} \\ $$$$\:\:\:\:\:\:\:\:\:=\:\mathrm{40}\frac{\mathrm{1}}{\mathrm{2}}\:{days}\:. \\ $$
Commented by mondodotto@gmail.com last updated on 17/Apr/18
$$\mathrm{thanx}\:\mathrm{be}\:\mathrm{blessed} \\ $$