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Question Number 95232 by bobhans last updated on 24/May/20
Commented by bobhans last updated on 24/May/20
i want compare with my answer
$$\mathrm{i}\:\mathrm{want}\:\mathrm{compare}\:\mathrm{with}\:\mathrm{my}\:\mathrm{answer} \\ $$
Commented by bobhans last updated on 24/May/20
the choice answer? (a) 5 day (b) 8 day (c) 10 day (d) 12 day
$$\mathrm{the}\:\mathrm{choice}\:\mathrm{answer}? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{5}\:\mathrm{day}\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{8}\:\mathrm{day}\: \\ $$$$\left(\mathrm{c}\right)\:\mathrm{10}\:\mathrm{day}\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{12}\:\mathrm{day} \\ $$
Commented by PRITHWISH SEN 2 last updated on 24/May/20
6m+8w=15⇒90m+120w=1⇒9m+12w=10 Ans- 10 days
$$\mathrm{6m}+\mathrm{8w}=\mathrm{15}\Rightarrow\mathrm{90m}+\mathrm{120w}=\mathrm{1}\Rightarrow\mathrm{9m}+\mathrm{12w}=\mathrm{10} \\ $$$$\mathrm{Ans}-\:\mathrm{10}\:\mathrm{days} \\ $$
Commented by Farruxjano last updated on 24/May/20
Ans: C
$$\:\:\:\: \\ $$$$\boldsymbol{{Ans}}:\:\:\:\boldsymbol{{C}} \\ $$
Commented by mr W last updated on 24/May/20
10 days is correct. if we don′t use math. eqn. but only human logic, we know the answer quickly: with 9 men and 12 women, we have (3/2) as much power as with 6 men and 8 women, therefore we need only (2/3) as much time as before. if we need 15 days before, then we need only 10 days now. if we double the power, i.e. with 12 men and 16 women, then we need only half of the time as before, i.e. 7.5 days. if we want to do the job in only 5 days, we must have triple power as before, i.e. we need 18 men and 24 women.
$$\mathrm{10}\:{days}\:{is}\:{correct}. \\ $$$${if}\:{we}\:{don}'{t}\:{use}\:{math}.\:{eqn}.\:{but}\:{only} \\ $$$${human}\:{logic},\:{we}\:{know}\:{the}\:{answer} \\ $$$${quickly}: \\ $$$${with}\:\mathrm{9}\:{men}\:{and}\:\mathrm{12}\:{women},\:{we}\:{have} \\ $$$$\frac{\mathrm{3}}{\mathrm{2}}\:{as}\:{much}\:{power}\:{as}\:{with}\:\mathrm{6}\:{men}\:{and} \\ $$$$\mathrm{8}\:{women},\:{therefore}\:{we}\:{need}\:{only}\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${as}\:{much}\:{time}\:{as}\:{before}.\:{if}\:{we}\:{need} \\ $$$$\mathrm{15}\:{days}\:{before},\:{then}\:{we}\:{need}\:{only} \\ $$$$\mathrm{10}\:{days}\:{now}. \\ $$$$ \\ $$$${if}\:{we}\:{double}\:{the}\:{power},\:{i}.{e}.\:{with} \\ $$$$\mathrm{12}\:{men}\:{and}\:\mathrm{16}\:{women},\:{then}\:{we}\:{need}\:{only} \\ $$$${half}\:{of}\:{the}\:{time}\:{as}\:{before},\:{i}.{e}.\:\mathrm{7}.\mathrm{5}\:{days}. \\ $$$$ \\ $$$${if}\:{we}\:{want}\:{to}\:{do}\:{the}\:{job}\:{in}\:{only}\:\mathrm{5}\:{days}, \\ $$$${we}\:{must}\:{have}\:{triple}\:{power}\:{as}\:{before}, \\ $$$${i}.{e}.\:{we}\:{need}\:\mathrm{18}\:{men}\:{and}\:\mathrm{24}\:{women}. \\ $$
Commented by bobhans last updated on 24/May/20
alright
$$\mathrm{alright} \\ $$
Answered by Farruxjano last updated on 24/May/20
Do you have any problem else?
$$\boldsymbol{{Do}}\:\boldsymbol{{you}}\:\boldsymbol{{have}}\:\boldsymbol{{any}}\:\boldsymbol{{problem}}\:\boldsymbol{{else}}? \\ $$
Commented by bobhans last updated on 24/May/20
do you mean the same type?
$$\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{the}\:\mathrm{same}\:\mathrm{type}? \\ $$
Answered by Farruxjano last updated on 24/May/20
Let: the speed of men is − v_1 and the woman − v_2 and the work − S. So, we get: (6v_1 +8v_2 )∙15=S ⇒ we must find:A=(S/(9v_1 +12v_2 ))=? (6v_1 +8v_2 )∙15=S⇒ (3v_1 +4v_2 )∙30=S⇒ ⇒ 3v_1 +4v_2 =(S/(30)) ∣×3⇒9v_1 +12v_2 =(S/(10))⇒ ⇒A=(S/(9v_1 +12v_2 ))=(S/(S/(10)))=10 days. I don′t know English perfect so I apologise
$$\boldsymbol{{Let}}:\:\boldsymbol{{the}}\:\boldsymbol{{speed}}\:\boldsymbol{{of}}\:\boldsymbol{{men}}\:\boldsymbol{{is}}\:−\:\boldsymbol{{v}}_{\mathrm{1}} \:\boldsymbol{{and}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{woman}}\:−\:\boldsymbol{{v}}_{\mathrm{2}} \:\boldsymbol{{and}}\:\boldsymbol{{the}}\:\boldsymbol{{work}}\:−\:\boldsymbol{{S}}.\:\boldsymbol{{So}},\:\boldsymbol{{we}}\:\boldsymbol{{get}}: \\ $$$$\left(\mathrm{6}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{8}\boldsymbol{{v}}_{\mathrm{2}} \right)\centerdot\mathrm{15}=\boldsymbol{{S}}\:\Rightarrow\:\boldsymbol{{we}}\:\boldsymbol{{must}}\:\boldsymbol{{find}}:\boldsymbol{{A}}=\frac{\boldsymbol{{S}}}{\mathrm{9}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{12}\boldsymbol{{v}}_{\mathrm{2}} }=? \\ $$$$\left(\mathrm{6}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{8}\boldsymbol{{v}}_{\mathrm{2}} \right)\centerdot\mathrm{15}=\boldsymbol{{S}}\Rightarrow\:\left(\mathrm{3}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{4}\boldsymbol{{v}}_{\mathrm{2}} \right)\centerdot\mathrm{30}=\boldsymbol{{S}}\Rightarrow \\ $$$$\Rightarrow\:\mathrm{3}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{4}\boldsymbol{{v}}_{\mathrm{2}} =\frac{\boldsymbol{{S}}}{\mathrm{30}}\:\mid×\mathrm{3}\Rightarrow\mathrm{9}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{12}\boldsymbol{{v}}_{\mathrm{2}} =\frac{\boldsymbol{{S}}}{\mathrm{10}}\Rightarrow \\ $$$$\Rightarrow\boldsymbol{{A}}=\frac{\boldsymbol{{S}}}{\mathrm{9}\boldsymbol{{v}}_{\mathrm{1}} +\mathrm{12}\boldsymbol{{v}}_{\mathrm{2}} }=\frac{\boldsymbol{{S}}}{\frac{\boldsymbol{{S}}}{\mathrm{10}}}=\mathrm{10}\:\boldsymbol{{days}}. \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{don}}'\boldsymbol{{t}}\:\boldsymbol{{know}}\:\boldsymbol{{English}}\:\boldsymbol{{perfect}}\:\boldsymbol{{so}} \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{apologise}} \\ $$
Answered by mr W last updated on 24/May/20
say a man can do m things each day, and a woman can do w things each day. for the job totally there are s things to do. 6 men and 9 women need 15 days, i.e. (6m+8w)15=s ...(i) say 9 men and 12 women need x days, i.e. (9m+12w)x=s ...(ii) (ii)/(i): ((3x)/(2×15))=1 ⇒x=10 days
$${say}\:{a}\:{man}\:{can}\:{do}\:\boldsymbol{{m}}\:{things}\:{each}\:{day}, \\ $$$${and}\:{a}\:{woman}\:{can}\:{do}\:\boldsymbol{{w}}\:{things}\:{each}\:{day}. \\ $$$${for}\:{the}\:{job}\:{totally}\:{there}\:{are}\:\boldsymbol{{s}}\:{things} \\ $$$${to}\:{do}. \\ $$$$\mathrm{6}\:{men}\:{and}\:\mathrm{9}\:{women}\:{need}\:\mathrm{15}\:{days},\:{i}.{e}. \\ $$$$\left(\mathrm{6}{m}+\mathrm{8}{w}\right)\mathrm{15}={s}\:\:\:…\left({i}\right) \\ $$$${say}\:\mathrm{9}\:{men}\:{and}\:\mathrm{12}\:{women}\:{need}\:{x}\:{days},\:{i}.{e}. \\ $$$$\left(\mathrm{9}{m}+\mathrm{12}{w}\right){x}={s}\:\:\:…\left({ii}\right) \\ $$$$\left({ii}\right)/\left({i}\right): \\ $$$$\frac{\mathrm{3}{x}}{\mathrm{2}×\mathrm{15}}=\mathrm{1} \\ $$$$\Rightarrow{x}=\mathrm{10}\:{days} \\ $$

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