Question Number 95232 by bobhans last updated on 24/May/20
Commented by bobhans last updated on 24/May/20
$$\mathrm{i}\:\mathrm{want}\:\mathrm{compare}\:\mathrm{with}\:\mathrm{my}\:\mathrm{answer} \\ $$
Commented by bobhans last updated on 24/May/20
$$\mathrm{the}\:\mathrm{choice}\:\mathrm{answer}? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{5}\:\mathrm{day}\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{8}\:\mathrm{day}\: \\ $$$$\left(\mathrm{c}\right)\:\mathrm{10}\:\mathrm{day}\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{12}\:\mathrm{day} \\ $$
Commented by PRITHWISH SEN 2 last updated on 24/May/20
$$\mathrm{6m}+\mathrm{8w}=\mathrm{15}\Rightarrow\mathrm{90m}+\mathrm{120w}=\mathrm{1}\Rightarrow\mathrm{9m}+\mathrm{12w}=\mathrm{10} \\ $$$$\mathrm{Ans}-\:\mathrm{10}\:\mathrm{days} \\ $$
Commented by Farruxjano last updated on 24/May/20
$$\:\:\:\: \\ $$$$\boldsymbol{{Ans}}:\:\:\:\boldsymbol{{C}} \\ $$
Commented by mr W last updated on 24/May/20
$$\mathrm{10}\:{days}\:{is}\:{correct}. \\ $$$${if}\:{we}\:{don}'{t}\:{use}\:{math}.\:{eqn}.\:{but}\:{only} \\ $$$${human}\:{logic},\:{we}\:{know}\:{the}\:{answer} \\ $$$${quickly}: \\ $$$${with}\:\mathrm{9}\:{men}\:{and}\:\mathrm{12}\:{women},\:{we}\:{have} \\ $$$$\frac{\mathrm{3}}{\mathrm{2}}\:{as}\:{much}\:{power}\:{as}\:{with}\:\mathrm{6}\:{men}\:{and} \\ $$$$\mathrm{8}\:{women},\:{therefore}\:{we}\:{need}\:{only}\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${as}\:{much}\:{time}\:{as}\:{before}.\:{if}\:{we}\:{need} \\ $$$$\mathrm{15}\:{days}\:{before},\:{then}\:{we}\:{need}\:{only} \\ $$$$\mathrm{10}\:{days}\:{now}. \\ $$$$ \\ $$$${if}\:{we}\:{double}\:{the}\:{power},\:{i}.{e}.\:{with} \\ $$$$\mathrm{12}\:{men}\:{and}\:\mathrm{16}\:{women},\:{then}\:{we}\:{need}\:{only} \\ $$$${half}\:{of}\:{the}\:{time}\:{as}\:{before},\:{i}.{e}.\:\mathrm{7}.\mathrm{5}\:{days}. \\ $$$$ \\ $$$${if}\:{we}\:{want}\:{to}\:{do}\:{the}\:{job}\:{in}\:{only}\:\mathrm{5}\:{days}, \\ $$$${we}\:{must}\:{have}\:{triple}\:{power}\:{as}\:{before}, \\ $$$${i}.{e}.\:{we}\:{need}\:\mathrm{18}\:{men}\:{and}\:\mathrm{24}\:{women}. \\ $$
Commented by bobhans last updated on 24/May/20
$$\mathrm{alright} \\ $$
Answered by Farruxjano last updated on 24/May/20
$$\boldsymbol{{Do}}\:\boldsymbol{{you}}\:\boldsymbol{{have}}\:\boldsymbol{{any}}\:\boldsymbol{{problem}}\:\boldsymbol{{else}}? \\ $$
Commented by bobhans last updated on 24/May/20
$$\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{the}\:\mathrm{same}\:\mathrm{type}? \\ $$
Answered by Farruxjano last updated on 24/May/20
$$\boldsymbol{{Let}}:\:\boldsymbol{{the}}\:\boldsymbol{{speed}}\:\boldsymbol{{of}}\:\boldsymbol{{men}}\:\boldsymbol{{is}}\:−\:\boldsymbol{{v}}_{\mathrm{1}} \:\boldsymbol{{and}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{woman}}\:−\:\boldsymbol{{v}}_{\mathrm{2}} \:\boldsymbol{{and}}\:\boldsymbol{{the}}\:\boldsymbol{{work}}\:−\:\boldsymbol{{S}}.\:\boldsymbol{{So}},\:\boldsymbol{{we}}\:\boldsymbol{{get}}: \\ $$$$\left(\mathrm{6}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{8}\boldsymbol{{v}}_{\mathrm{2}} \right)\centerdot\mathrm{15}=\boldsymbol{{S}}\:\Rightarrow\:\boldsymbol{{we}}\:\boldsymbol{{must}}\:\boldsymbol{{find}}:\boldsymbol{{A}}=\frac{\boldsymbol{{S}}}{\mathrm{9}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{12}\boldsymbol{{v}}_{\mathrm{2}} }=? \\ $$$$\left(\mathrm{6}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{8}\boldsymbol{{v}}_{\mathrm{2}} \right)\centerdot\mathrm{15}=\boldsymbol{{S}}\Rightarrow\:\left(\mathrm{3}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{4}\boldsymbol{{v}}_{\mathrm{2}} \right)\centerdot\mathrm{30}=\boldsymbol{{S}}\Rightarrow \\ $$$$\Rightarrow\:\mathrm{3}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{4}\boldsymbol{{v}}_{\mathrm{2}} =\frac{\boldsymbol{{S}}}{\mathrm{30}}\:\mid×\mathrm{3}\Rightarrow\mathrm{9}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{12}\boldsymbol{{v}}_{\mathrm{2}} =\frac{\boldsymbol{{S}}}{\mathrm{10}}\Rightarrow \\ $$$$\Rightarrow\boldsymbol{{A}}=\frac{\boldsymbol{{S}}}{\mathrm{9}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{12}\boldsymbol{{v}}_{\mathrm{2}} }=\frac{\boldsymbol{{S}}}{\frac{\boldsymbol{{S}}}{\mathrm{10}}}=\mathrm{10}\:\boldsymbol{{days}}. \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{don}}'\boldsymbol{{t}}\:\boldsymbol{{know}}\:\boldsymbol{{English}}\:\boldsymbol{{perfect}}\:\boldsymbol{{so}} \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{apologise}} \\ $$
Answered by mr W last updated on 24/May/20
$${say}\:{a}\:{man}\:{can}\:{do}\:\boldsymbol{{m}}\:{things}\:{each}\:{day}, \\ $$$${and}\:{a}\:{woman}\:{can}\:{do}\:\boldsymbol{{w}}\:{things}\:{each}\:{day}. \\ $$$${for}\:{the}\:{job}\:{totally}\:{there}\:{are}\:\boldsymbol{{s}}\:{things} \\ $$$${to}\:{do}. \\ $$$$\mathrm{6}\:{men}\:{and}\:\mathrm{9}\:{women}\:{need}\:\mathrm{15}\:{days},\:{i}.{e}. \\ $$$$\left(\mathrm{6}{m}+\mathrm{8}{w}\right)\mathrm{15}={s}\:\:\:...\left({i}\right) \\ $$$${say}\:\mathrm{9}\:{men}\:{and}\:\mathrm{12}\:{women}\:{need}\:{x}\:{days},\:{i}.{e}. \\ $$$$\left(\mathrm{9}{m}+\mathrm{12}{w}\right){x}={s}\:\:\:...\left({ii}\right) \\ $$$$\left({ii}\right)/\left({i}\right): \\ $$$$\frac{\mathrm{3}{x}}{\mathrm{2}×\mathrm{15}}=\mathrm{1} \\ $$$$\Rightarrow{x}=\mathrm{10}\:{days} \\ $$