Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 20992 by NECx last updated on 09/Sep/17

Commented by NECx last updated on 09/Sep/17

please help guys

$$\mathrm{please}\:\mathrm{help}\:\mathrm{guys} \\ $$

Answered by $@ty@m last updated on 10/Sep/17

Let there be x girls. ⇒no. of boys=((110)/(100))x ⇒no. of children, i.e. no. of boys+girls=x+((110)/(100))x Again, Let no. of men=y ⇒no. of women=((115)/(100))y ⇒no. of adults=((215)/(100))y −(2) ATQ ((215)/(100))y×((120)/(100))=((210)/(100))x ⇒x=((215)/(100))×((120)/(210))y ⇒x=((43)/(35))y −−−(3) ∴ no. of boys=((110)/(100))x=((110)/(100))×((43)/(35))y =((473)/(350))y −−(4) Given, population<6000 ((210)/(100))x+((215)/(100))y<6000 210x+215y<600000 210×((43)/(35))y+215y<600000 258y+215y<600000 473y<600000 y<1268.5 −−(5) (2)⇒y∣20 (3)⇒y∣35 (4)⇒y∣350 LCM(20,35,350)=700 ∴ (5)⇒ y=700 ⇒no. of men=700 ⇒no. of women=((115)/(100))×700=805 no. of girls=((43)/(35))×700=860 no. of boys=((473)/(350))×700=946

$${Let}\:{there}\:{be}\:{x}\:{girls}. \\ $$$$\Rightarrow{no}.\:{of}\:{boys}=\frac{\mathrm{110}}{\mathrm{100}}{x} \\ $$$$\Rightarrow{no}.\:{of}\:{children},\:{i}.{e}. \\ $$$$\:\:\:\:\:\:\:\:{no}.\:{of}\:{boys}+{girls}={x}+\frac{\mathrm{110}}{\mathrm{100}}{x} \\ $$$$\:\:\:\:\: \\ $$$${Again}, \\ $$$${Let}\:{no}.\:{of}\:{men}={y} \\ $$$$\Rightarrow{no}.\:{of}\:{women}=\frac{\mathrm{115}}{\mathrm{100}}{y}\: \\ $$$$\Rightarrow{no}.\:{of}\:{adults}=\frac{\mathrm{215}}{\mathrm{100}}{y}\:\:−\left(\mathrm{2}\right) \\ $$$${ATQ} \\ $$$$\frac{\mathrm{215}}{\mathrm{100}}{y}×\frac{\mathrm{120}}{\mathrm{100}}=\frac{\mathrm{210}}{\mathrm{100}}{x} \\ $$$$\Rightarrow{x}=\frac{\mathrm{215}}{\mathrm{100}}×\frac{\mathrm{120}}{\mathrm{210}}{y} \\ $$$$\Rightarrow{x}=\frac{\mathrm{43}}{\mathrm{35}}{y}\:−−−\left(\mathrm{3}\right) \\ $$$$\therefore\:{no}.\:{of}\:{boys}=\frac{\mathrm{110}}{\mathrm{100}}{x}=\frac{\mathrm{110}}{\mathrm{100}}×\frac{\mathrm{43}}{\mathrm{35}}{y} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{473}}{\mathrm{350}}{y}\:−−\left(\mathrm{4}\right) \\ $$$${Given}, \\ $$$${population}<\mathrm{6000} \\ $$$$\frac{\mathrm{210}}{\mathrm{100}}{x}+\frac{\mathrm{215}}{\mathrm{100}}{y}<\mathrm{6000} \\ $$$$\mathrm{210}{x}+\mathrm{215}{y}<\mathrm{600000} \\ $$$$\mathrm{210}×\frac{\mathrm{43}}{\mathrm{35}}{y}+\mathrm{215}{y}<\mathrm{600000} \\ $$$$\mathrm{258}{y}+\mathrm{215}{y}<\mathrm{600000} \\ $$$$\mathrm{473}{y}<\mathrm{600000} \\ $$$${y}<\mathrm{1268}.\mathrm{5}\:−−\left(\mathrm{5}\right) \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\Rightarrow{y}\mid\mathrm{20} \\ $$$$\left(\mathrm{3}\right)\Rightarrow{y}\mid\mathrm{35} \\ $$$$\left(\mathrm{4}\right)\Rightarrow{y}\mid\mathrm{350} \\ $$$${LCM}\left(\mathrm{20},\mathrm{35},\mathrm{350}\right)=\mathrm{700} \\ $$$$\therefore\:\left(\mathrm{5}\right)\Rightarrow\:{y}=\mathrm{700} \\ $$$$\Rightarrow{no}.\:{of}\:{men}=\mathrm{700} \\ $$$$\Rightarrow{no}.\:{of}\:{women}=\frac{\mathrm{115}}{\mathrm{100}}×\mathrm{700}=\mathrm{805} \\ $$$${no}.\:{of}\:{girls}=\frac{\mathrm{43}}{\mathrm{35}}×\mathrm{700}=\mathrm{860} \\ $$$${no}.\:{of}\:{boys}=\frac{\mathrm{473}}{\mathrm{350}}×\mathrm{700}=\mathrm{946} \\ $$

Commented by NECx last updated on 10/Sep/17

wow..... this is great sir. i′m most grateful sir.Words cant express how happy I am. Thank you

$$\mathrm{wow}.....\:\mathrm{this}\:\mathrm{is}\:\mathrm{great}\:\mathrm{sir}. \\ $$$$\mathrm{i}'\mathrm{m}\:\mathrm{most}\:\mathrm{grateful}\:\mathrm{sir}.\mathrm{Words}\:\mathrm{cant} \\ $$$$\mathrm{express}\:\mathrm{how}\:\mathrm{happy}\:\mathrm{I}\:\mathrm{am}.\:\mathrm{Thank} \\ $$$$\mathrm{you} \\ $$

Commented by NECx last updated on 10/Sep/17

what do you mean by (2)⇒y∣20 (3)⇒y∣35 (4)⇒y∣350 l.c.m(20,35,350)=700

$$\mathrm{what}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{by} \\ $$$$\left(\mathrm{2}\right)\Rightarrow\mathrm{y}\mid\mathrm{20} \\ $$$$\left(\mathrm{3}\right)\Rightarrow\mathrm{y}\mid\mathrm{35} \\ $$$$\left(\mathrm{4}\right)\Rightarrow\mathrm{y}\mid\mathrm{350} \\ $$$$\mathrm{l}.\mathrm{c}.\mathrm{m}\left(\mathrm{20},\mathrm{35},\mathrm{350}\right)=\mathrm{700} \\ $$

Commented by $@ty@m last updated on 10/Sep/17

∵ y is no. of men ∴y∈N Similarly no. of adults=((215)/(100))y∈N which is possible only if y is a multiple of 20. that is what I meant by (2)⇒y∣20 and likewise for other two expessions. Further, to fulfill the three conditions simltaneously we′ll have to find the Least Common Multiple (LCM) of 20, 35 and 350 which is 700. ∴y∈{700, 1400, ......} but in ineqation(5), we have y<1268.5 ⇒y=700 Are all your doubts clear now?

$$\because\:{y}\:{is}\:{no}.\:{of}\:{men} \\ $$$$\therefore{y}\in\mathrm{N} \\ $$$$\:{Similarly}\:{no}.\:{of}\:{adults}=\frac{\mathrm{215}}{\mathrm{100}}{y}\in\mathrm{N} \\ $$$${which}\:{is}\:{possible}\:{only}\:{if}\:{y}\:{is}\:{a}\:{multiple}\:{of}\:\mathrm{20}. \\ $$$${that}\:{is}\:{what}\:{I}\:{meant}\:{by}\: \\ $$$$\left(\mathrm{2}\right)\Rightarrow\mathrm{y}\mid\mathrm{20}\: \\ $$$${and}\:{likewise}\:{for}\:{other}\:{two}\:{expessions}. \\ $$$${Further},\:{to}\:{fulfill}\:{the}\:{three}\: \\ $$$${conditions}\:{simltaneously} \\ $$$${we}'{ll}\:{have}\:{to}\:{find}\:{the}\:{Least}\:{Common} \\ $$$${Multiple}\:\left({LCM}\right)\:{of}\:\mathrm{20},\:\mathrm{35}\:{and}\:\mathrm{350} \\ $$$${which}\:{is}\:\mathrm{700}. \\ $$$$\therefore{y}\in\left\{\mathrm{700},\:\mathrm{1400},\:......\right\} \\ $$$${but}\:{in}\:{ineqation}\left(\mathrm{5}\right),\:{we}\:{have} \\ $$$${y}<\mathrm{1268}.\mathrm{5} \\ $$$$\Rightarrow{y}=\mathrm{700} \\ $$$${Are}\:{all}\:{your}\:{doubts}\:{clear}\:{now}? \\ $$

Commented by NECx last updated on 10/Sep/17

yeah.... i understand . please which topic in maths does this question come from?

$$\mathrm{yeah}....\:\mathrm{i}\:\mathrm{understand}\:. \\ $$$$\mathrm{please}\:\mathrm{which}\:\mathrm{topic}\:\mathrm{in}\:\mathrm{maths}\:\mathrm{does} \\ $$$$\mathrm{this}\:\mathrm{question}\:\mathrm{come}\:\mathrm{from}? \\ $$

Commented by $@ty@m last updated on 10/Sep/17

HaaHaaHaa the same question I was going to ask you.... It seems to be “Applcation of ineqality” but actually perception of “Percentage” and “Number Theory” are also involved. More than theory, it needs logic to solve.

$${HaaHaaHaa} \\ $$$${the}\:{same}\:{question}\:{I}\:{was}\:{going} \\ $$$${to}\:{ask}\:{you}.... \\ $$$${It}\:{seems}\:{to}\:{be}\:``{Applcation}\:{of}\:{ineqality}'' \\ $$$${but}\:{actually}\:{perception}\:{of}\:``{Percentage}''\:{and} \\ $$$$``{Number}\:{Theory}''\:{are}\:{also}\:{involved}. \\ $$$${More}\:{than}\:{theory},\:{it}\:{needs}\:{logic} \\ $$$${to}\:{solve}. \\ $$

Commented by NECx last updated on 10/Sep/17

hmmmm.... i hear you sir.

$$\mathrm{hmmmm}....\:\mathrm{i}\:\mathrm{hear}\:\mathrm{you}\:\mathrm{sir}. \\ $$

Answered by mrW1 last updated on 10/Sep/17

C=children in % A=adult in % B=boys in % G=girls in % C+A=100%=1 C=1.2×A ⇒C=(6/(11)) ⇒A=(5/(11)) B+G=C=(6/(11)) B=1.1×G ⇒B=((22)/(77)) ⇒G=((20)/(77)) W+M=A=(5/(11)) W=1.15×M ⇒W=((115)/(473)) ⇒M=((100)/(473)) let N=total population ⇒Boys=((22)/(77))N=22×(N/(77)) ⇒Girls=((20)/(77))N=20×(N/(77)) ⇒Women=((115)/(473))N=115×(N/(473)) ⇒Men=((100)/(473))N=100×(N/(473)) LCM(77,473)=3311 ⇒N=3311k with k∈N ⇒Boys=22×((3311k)/(77))=946k ⇒Girls=20×((3311k)/(77))=860k ⇒Women=115×((3311k)/(473))=805k ⇒Men=100×((3311k)/(473))=700k since N<6000, ⇒k=1 ⇒946 boys, 860 girls, 805 women, 700 men

$$\mathrm{C}=\mathrm{children}\:\mathrm{in}\:\% \\ $$$$\mathrm{A}=\mathrm{adult}\:\mathrm{in}\:\% \\ $$$$\mathrm{B}=\mathrm{boys}\:\mathrm{in}\:\% \\ $$$$\mathrm{G}=\mathrm{girls}\:\mathrm{in}\:\% \\ $$$$ \\ $$$$\mathrm{C}+\mathrm{A}=\mathrm{100\%}=\mathrm{1} \\ $$$$\mathrm{C}=\mathrm{1}.\mathrm{2}×\mathrm{A} \\ $$$$\Rightarrow\mathrm{C}=\frac{\mathrm{6}}{\mathrm{11}} \\ $$$$\Rightarrow\mathrm{A}=\frac{\mathrm{5}}{\mathrm{11}} \\ $$$$ \\ $$$$\mathrm{B}+\mathrm{G}=\mathrm{C}=\frac{\mathrm{6}}{\mathrm{11}} \\ $$$$\mathrm{B}=\mathrm{1}.\mathrm{1}×\mathrm{G} \\ $$$$\Rightarrow\mathrm{B}=\frac{\mathrm{22}}{\mathrm{77}} \\ $$$$\Rightarrow\mathrm{G}=\frac{\mathrm{20}}{\mathrm{77}} \\ $$$$ \\ $$$$\mathrm{W}+\mathrm{M}=\mathrm{A}=\frac{\mathrm{5}}{\mathrm{11}} \\ $$$$\mathrm{W}=\mathrm{1}.\mathrm{15}×\mathrm{M} \\ $$$$\Rightarrow\mathrm{W}=\frac{\mathrm{115}}{\mathrm{473}} \\ $$$$\Rightarrow\mathrm{M}=\frac{\mathrm{100}}{\mathrm{473}} \\ $$$$ \\ $$$$\mathrm{let}\:\mathrm{N}=\mathrm{total}\:\mathrm{population} \\ $$$$\Rightarrow\mathrm{Boys}=\frac{\mathrm{22}}{\mathrm{77}}\mathrm{N}=\mathrm{22}×\frac{\mathrm{N}}{\mathrm{77}} \\ $$$$\Rightarrow\mathrm{Girls}=\frac{\mathrm{20}}{\mathrm{77}}\mathrm{N}=\mathrm{20}×\frac{\mathrm{N}}{\mathrm{77}} \\ $$$$\Rightarrow\mathrm{Women}=\frac{\mathrm{115}}{\mathrm{473}}\mathrm{N}=\mathrm{115}×\frac{\mathrm{N}}{\mathrm{473}} \\ $$$$\Rightarrow\mathrm{Men}=\frac{\mathrm{100}}{\mathrm{473}}\mathrm{N}=\mathrm{100}×\frac{\mathrm{N}}{\mathrm{473}} \\ $$$$ \\ $$$$\mathrm{LCM}\left(\mathrm{77},\mathrm{473}\right)=\mathrm{3311} \\ $$$$\Rightarrow\mathrm{N}=\mathrm{3311k}\:\mathrm{with}\:\mathrm{k}\in\mathbb{N} \\ $$$$\Rightarrow\mathrm{Boys}=\mathrm{22}×\frac{\mathrm{3311k}}{\mathrm{77}}=\mathrm{946k} \\ $$$$\Rightarrow\mathrm{Girls}=\mathrm{20}×\frac{\mathrm{3311k}}{\mathrm{77}}=\mathrm{860k} \\ $$$$\Rightarrow\mathrm{Women}=\mathrm{115}×\frac{\mathrm{3311k}}{\mathrm{473}}=\mathrm{805k} \\ $$$$\Rightarrow\mathrm{Men}=\mathrm{100}×\frac{\mathrm{3311k}}{\mathrm{473}}=\mathrm{700k} \\ $$$$ \\ $$$$\mathrm{since}\:\mathrm{N}<\mathrm{6000},\:\Rightarrow\mathrm{k}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{946}\:\mathrm{boys},\:\mathrm{860}\:\mathrm{girls},\:\mathrm{805}\:\mathrm{women},\:\mathrm{700}\:\mathrm{men} \\ $$

Commented by NECx last updated on 10/Sep/17

thank you sir

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

Commented by NECx last updated on 10/Sep/17

sorry but i really need to ask this; why was it necessary to find the LCM of the denominators? Thanks for always helping.

$$\mathrm{sorry}\:\mathrm{but}\:\mathrm{i}\:\mathrm{really}\:\mathrm{need}\:\mathrm{to}\:\mathrm{ask}\:\mathrm{this}; \\ $$$$ \\ $$$$\mathrm{why}\:\mathrm{was}\:\mathrm{it}\:\mathrm{necessary}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{LCM}\:\mathrm{of}\:\mathrm{the}\:\mathrm{denominators}? \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thanks}\:\mathrm{for}\:\mathrm{always}\:\mathrm{helping}. \\ $$

Commented by mrW1 last updated on 11/Sep/17

(N/(77)) and (N/(473)) must be integer, i.e. N must be a multiple of 77 and 473. ⇒N=LCM(77,473)×k=3311k

$$\frac{\mathrm{N}}{\mathrm{77}}\:\mathrm{and}\:\frac{\mathrm{N}}{\mathrm{473}}\:\mathrm{must}\:\mathrm{be}\:\mathrm{integer},\:\mathrm{i}.\mathrm{e}. \\ $$$$\mathrm{N}\:\mathrm{must}\:\mathrm{be}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{77}\:\mathrm{and}\:\mathrm{473}. \\ $$$$\Rightarrow\mathrm{N}=\mathrm{LCM}\left(\mathrm{77},\mathrm{473}\right)×\mathrm{k}=\mathrm{3311k} \\ $$

Answered by ajfour last updated on 10/Sep/17

((boy)/(girl))=((11x)/(10x)) ; ((women)/(men))=((23y)/(20y)) ((children)/(adult))=(6/5). ⇒ ((21x)/(43y))=(6/5) ⇒ 35x=86y Also 21x+43y < 6000 or 42x+35x <12000 x<((12000)/(77)) <155((65)/(77)) x is also a multiple of 86, so x=86 , y=35 no. of boys = 11x=946 no. of girls = 10x=860 no. of women = 23y=805 no. of men = 20y=700 total population =3311 .

$$\frac{{boy}}{{girl}}=\frac{\mathrm{11}{x}}{\mathrm{10}{x}}\:;\:\:\frac{{women}}{{men}}=\frac{\mathrm{23}{y}}{\mathrm{20}{y}} \\ $$$$\frac{{children}}{{adult}}=\frac{\mathrm{6}}{\mathrm{5}}. \\ $$$$\Rightarrow\:\:\:\:\:\frac{\mathrm{21}{x}}{\mathrm{43}{y}}=\frac{\mathrm{6}}{\mathrm{5}}\: \\ $$$$\Rightarrow\:\:\:\:\:\:\mathrm{35}{x}=\mathrm{86}{y} \\ $$$$\:{Also}\:\:\:\:\mathrm{21}{x}+\mathrm{43}{y}\:<\:\mathrm{6000} \\ $$$${or}\:\:\:\:\:\:\:\:\:\:\mathrm{42}{x}+\mathrm{35}{x}\:<\mathrm{12000} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}<\frac{\mathrm{12000}}{\mathrm{77}}\:<\mathrm{155}\frac{\mathrm{65}}{\mathrm{77}} \\ $$$${x}\:{is}\:{also}\:{a}\:{multiple}\:{of}\:\mathrm{86},\:{so} \\ $$$$\:\:{x}=\mathrm{86}\:,\:{y}=\mathrm{35} \\ $$$${no}.\:{of}\:{boys}\:=\:\mathrm{11}{x}=\mathrm{946} \\ $$$${no}.\:{of}\:{girls}\:=\:\mathrm{10}{x}=\mathrm{860} \\ $$$${no}.\:{of}\:{women}\:=\:\mathrm{23}{y}=\mathrm{805} \\ $$$${no}.\:{of}\:{men}\:=\:\mathrm{20}{y}=\mathrm{700} \\ $$$${total}\:{population}\:=\mathrm{3311}\:. \\ $$

Commented by NECx last updated on 10/Sep/17

thank you sir

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

Commented by $@ty@m last updated on 10/Sep/17

BEST SOLUTION

$$\mathbb{BEST}\:\mathbb{SOLUTION} \\ $$

Commented by NECx last updated on 10/Sep/17

seems to be a really nice solution for others but i′m really confused. This is my question here guys , 35x=86y .....how?

$$\mathrm{seems}\:\mathrm{to}\:\mathrm{be}\:\mathrm{a}\:\mathrm{really}\:\mathrm{nice}\:\mathrm{solution} \\ $$$$\mathrm{for}\:\mathrm{others}\:\mathrm{but}\:\mathrm{i}'\mathrm{m}\:\mathrm{really}\:\mathrm{confused}. \\ $$$$\mathrm{This}\:\mathrm{is}\:\mathrm{my}\:\mathrm{question}\:\mathrm{here}\:\mathrm{guys}\:, \\ $$$$\mathrm{35x}=\mathrm{86y}\:\:\:\:\:\:\:\:.....\mathrm{how}? \\ $$

Commented by ajfour last updated on 11/Sep/17

follows from line before ..

$${follows}\:{from}\:{line}\:{before}\:.. \\ $$

Commented by NECx last updated on 11/Sep/17

oh... its clear

$$\mathrm{oh}...\:\mathrm{its}\:\mathrm{clear} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com