Question Number 95294 by i jagooll last updated on 24/May/20
$$\mathrm{3}\:\mathrm{men},\:\mathrm{4}\:\mathrm{women}\:\&\:\mathrm{6}\:\mathrm{boy}\:\mathrm{together} \\ $$$$\mathrm{working}\:\mathrm{a}\:\mathrm{job}\:\mathrm{within}\:\mathrm{25}\:\mathrm{day}.\:\mathrm{if}\:\mathrm{2}\:\mathrm{men}\: \\ $$$$,\:\mathrm{3}\:\mathrm{women}\:\mathrm{and}\:\mathrm{4}\:\mathrm{boy}\:\mathrm{working}\:\mathrm{the}\: \\ $$$$\mathrm{same}\:\mathrm{job},\:\mathrm{complete}\:\mathrm{in}\:? \\ $$
Commented by mr W last updated on 24/May/20
$${we}\:{can}\:{not}\:{determine},\:{because}\:{with} \\ $$$${the}\:{given}\:{condition}\:{we}\:{can}'{t}\:{know} \\ $$$${the}\:{working}\:{rate}\:{of}\:\mathrm{2}\:{men},\:\mathrm{3}\:{women} \\ $$$${and}\:\mathrm{4}\:{boys}. \\ $$
Commented by PRITHWISH SEN 2 last updated on 24/May/20
$$\mathrm{let}\:\mathrm{2}\boldsymbol{\mathrm{m}}+\mathrm{3}\boldsymbol{\mathrm{w}}+\mathrm{4}\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{x}}…\left(\mathrm{i}\right) \\ $$$$\mathrm{and}\:\mathrm{we}\:\mathrm{get} \\ $$$$\mathrm{3m}+\mathrm{4w}+\mathrm{6b}=\mathrm{25}\Rightarrow\mathrm{75m}+\mathrm{100w}+\mathrm{150b}=\mathrm{1} \\ $$$$\Rightarrow\frac{\mathrm{75}}{\mathrm{x}}\mathrm{m}+\frac{\mathrm{100}}{\mathrm{x}}\mathrm{w}+\frac{\mathrm{150}}{\mathrm{x}}\mathrm{b}=\mathrm{x}….\left(\mathrm{ii}\right) \\ $$$$\mathrm{now}\:\mathrm{compairing}\:\left(\mathrm{i}\right)\:\&\left(\mathrm{ii}\right)\:\mathrm{we}\:\mathrm{get} \\ $$$$\frac{\mathrm{75}}{\mathrm{x}}=\mathrm{2}\Rightarrow\boldsymbol{\mathrm{x}}=\frac{\mathrm{75}}{\mathrm{2}} \\ $$$$\frac{\mathrm{100}}{\boldsymbol{\mathrm{x}}}=\mathrm{3}\Rightarrow\boldsymbol{\mathrm{x}}=\frac{\mathrm{100}}{\mathrm{3}} \\ $$$$\frac{\mathrm{150}}{\boldsymbol{\mathrm{x}}}=\mathrm{4}\Rightarrow\boldsymbol{\mathrm{x}}=\frac{\mathrm{75}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{question}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{inconsistent}}\:\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{something}} \\ $$$$\boldsymbol{\mathrm{wrong}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{question}}.\:\boldsymbol{\mathrm{I}}\:\boldsymbol{\mathrm{don}}'\boldsymbol{\mathrm{t}}\:\boldsymbol{\mathrm{think}}\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{is}} \\ $$$$\boldsymbol{\mathrm{solvable}}. \\ $$
Answered by bobhans last updated on 24/May/20
$$\frac{\mathrm{1}}{{x}}\:\:=\:\frac{\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{4}}+\frac{\mathrm{4}}{\mathrm{6}}}{\mathrm{25}}\Rightarrow{x}\:=\:\frac{\mathrm{25}}{\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{4}}+\frac{\mathrm{2}}{\mathrm{3}}} \\ $$$${x}\:=\:\frac{\mathrm{25}}{\frac{\mathrm{4}}{\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{4}}}\:=\:\frac{\mathrm{25}×\mathrm{12}}{\mathrm{16}+\mathrm{9}}\:=\:\mathrm{12}\:{days} \\ $$
Commented by bobhans last updated on 24/May/20
$$\mathrm{please}\:\mathrm{check} \\ $$
Commented by mr W last updated on 24/May/20
$${can}\:{not}\:{be}\:{correct}!\:{with}\:{more}\:{people} \\ $$$${in}\:{the}\:{past}\:{we}\:{needed}\:\mathrm{25}\:{days},\:{now} \\ $$$${we}\:{have}\:{less}\:{people}\:{and}\:{we}\:{need}\:{even} \\ $$$${less}\:{time}\:{than}\:{before}? \\ $$
Commented by bobhans last updated on 24/May/20
$$\mathrm{this}\:\mathrm{means}\:\mathrm{the}\:\mathrm{problem}\:\mathrm{is}\:\mathrm{not}\:\mathrm{complete}?\: \\ $$$$\mathrm{really}? \\ $$
Commented by mr W last updated on 24/May/20
$${correct},\:{it}'{s}\:{not}\:{solvable}\:{with}\:{given} \\ $$$${info}. \\ $$
Commented by i jagooll last updated on 24/May/20
ok sir. thank you for the discussion