Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 174552 by Tawa11 last updated on 03/Aug/22

Commented by Rasheed.Sindhi last updated on 04/Aug/22

n=12 ; Please confirm the answer.

$$\mathrm{n}=\mathrm{12}\:;\:\mathrm{Please}\:\mathrm{confirm}\:\mathrm{the}\:\mathrm{answer}. \\ $$

Commented by Tawa11 last updated on 04/Aug/22

I don′t know the answer sir. please workings to follow.

$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{sir}. \\ $$$$\mathrm{please}\:\mathrm{workings}\:\mathrm{to}\:\mathrm{follow}. \\ $$

Commented by Tawa11 last updated on 04/Aug/22

Someone said: 24 approximately sir.

$$\mathrm{Someone}\:\mathrm{said}:\:\:\mathrm{24}\:\mathrm{approximately}\:\mathrm{sir}. \\ $$

Answered by Rasheed.Sindhi last updated on 05/Aug/22

AnOther way t is only for comparison its value doesn′t matter. Let for convenience t=gcd(46,69)=23 Number of vegitables per minute determinant (((rad. ),(cucum.),(onions),(okra )),((((46)/(23))=2),(((46)/(23))=2),(((69)/(23))=3),(((69)/(23))=3))) Number of minutes per vegitable determinant (((rad. ),(cucum.),(onions),(okra )),((((23)/(46))=(1/2)),(((23)/(46))=(1/2)),(((23)/(69))=(1/3)),(((23)/(69))=(1/3)))) First k minutes k/4 minutes for each vegitable determinant ((,(rad. ),(cucu.),(onions),(okra )),((per min.),2,2,3,3),((in (k/4) mins),(((2k)/4)=(k/2)),(((2k)/4)=(k/2)),((3k)/4),((3k)/4))) 2((k/2))+2(((3k)/4))=((5k)/2) vegitables. Next k minutes n+n+n+n=4n vegitables time in each vegitable: determinant ((,(rad. ),(cucum.),(onions),(okra )),((per veg._(time) ),(1/2),(1/2),(1/3),(1/3)),((time in_(n vegs) ),(n/2),(n/2),(n/3),(n/3))) total time: 2((n/2))+2((n/3))=((5n)/3)=k In 2k minutes total vegitables: ((5k)/2)+4n=98 (5/2)∙((5n)/3)+4n=98 [∵ k=((5n)/3)] ((49n)/6)=98 n=((98×6)/(49))=12

$$\mathrm{AnOther}\:\mathrm{way} \\ $$$$\boldsymbol{\mathrm{t}}\:\mathrm{is}\:\mathrm{only}\:\mathrm{for}\:\mathrm{comparison}\:\mathrm{its}\:\mathrm{value}\: \\ $$$$\mathrm{doesn}'\mathrm{t}\:\mathrm{matter}. \\ $$$$\mathrm{Let}\:\mathrm{for}\:\mathrm{convenience}\:\mathrm{t}=\mathrm{gcd}\left(\mathrm{46},\mathrm{69}\right)=\mathrm{23} \\ $$$$\underline{\mathrm{Number}\:\mathrm{of}\:\mathrm{vegitables}\:\mathrm{per}\:\mathrm{minute}} \\ $$$$\begin{array}{|c|c|}{\mathrm{rad}.\:\:\:\:}&\hline{\mathrm{cucum}.}&\hline{\mathrm{onions}}&\hline{\mathrm{okra}\:\:}\\{\frac{\mathrm{46}}{\mathrm{23}}=\mathrm{2}}&\hline{\frac{\mathrm{46}}{\mathrm{23}}=\mathrm{2}}&\hline{\frac{\mathrm{69}}{\mathrm{23}}=\mathrm{3}}&\hline{\frac{\mathrm{69}}{\mathrm{23}}=\mathrm{3}}\\\hline\end{array}\: \\ $$$$ \\ $$$$\underline{\mathrm{Number}\:\mathrm{of}\:\mathrm{minutes}\:\mathrm{per}\:\mathrm{vegitable}} \\ $$$$\begin{array}{|c|c|}{\mathrm{rad}.\:\:\:\:}&\hline{\mathrm{cucum}.}&\hline{\mathrm{onions}}&\hline{\mathrm{okra}\:\:}\\{\frac{\mathrm{23}}{\mathrm{46}}=\frac{\mathrm{1}}{\mathrm{2}}}&\hline{\frac{\mathrm{23}}{\mathrm{46}}=\frac{\mathrm{1}}{\mathrm{2}}}&\hline{\frac{\mathrm{23}}{\mathrm{69}}=\frac{\mathrm{1}}{\mathrm{3}}}&\hline{\frac{\mathrm{23}}{\mathrm{69}}=\frac{\mathrm{1}}{\mathrm{3}}}\\\hline\end{array}\: \\ $$$$ \\ $$$$\underline{\mathrm{First}\:\mathrm{k}\:\mathrm{minutes}} \\ $$$$\mathrm{k}/\mathrm{4}\:\mathrm{minutes}\:\mathrm{for}\:\mathrm{each}\:\mathrm{vegitable} \\ $$$$\begin{array}{|c|c|c|}{}&\hline{\mathrm{rad}.\:\:\:\:}&\hline{\mathrm{cucu}.}&\hline{\mathrm{onions}}&\hline{\mathrm{okra}\:\:}\\{\mathrm{per}\:\mathrm{min}.}&\hline{\mathrm{2}}&\hline{\mathrm{2}}&\hline{\mathrm{3}}&\hline{\mathrm{3}}\\{\mathrm{in}\:\frac{\mathrm{k}}{\mathrm{4}}\:\mathrm{mins}}&\hline{\frac{\mathrm{2k}}{\mathrm{4}}=\frac{\mathrm{k}}{\mathrm{2}}}&\hline{\frac{\mathrm{2k}}{\mathrm{4}}=\frac{\mathrm{k}}{\mathrm{2}}}&\hline{\frac{\mathrm{3k}}{\mathrm{4}}}&\hline{\frac{\mathrm{3k}}{\mathrm{4}}}\\\hline\end{array}\: \\ $$$$\mathrm{2}\left(\frac{\mathrm{k}}{\mathrm{2}}\right)+\mathrm{2}\left(\frac{\mathrm{3k}}{\mathrm{4}}\right)=\frac{\mathrm{5k}}{\mathrm{2}}\:\:\mathrm{vegitables}. \\ $$$$\underline{\mathrm{Next}\:\mathrm{k}\:\mathrm{minutes}} \\ $$$$\:\mathrm{n}+\mathrm{n}+\mathrm{n}+\mathrm{n}=\mathrm{4n}\:\mathrm{vegitables} \\ $$$$\:\mathrm{time}\:\mathrm{in}\:\mathrm{each}\:\mathrm{vegitable}: \\ $$$$\begin{array}{|c|c|c|}{}&\hline{\mathrm{rad}.\:\:\:\:}&\hline{\mathrm{cucum}.}&\hline{\mathrm{onions}}&\hline{\mathrm{okra}\:\:}\\{\underset{\mathrm{time}} {\mathrm{per}\:\mathrm{veg}.}}&\hline{\mathrm{1}/\mathrm{2}}&\hline{\mathrm{1}/\mathrm{2}}&\hline{\mathrm{1}/\mathrm{3}}&\hline{\mathrm{1}/\mathrm{3}}\\{\underset{\mathrm{n}\:\mathrm{vegs}} {\mathrm{time}\:\mathrm{in}}}&\hline{\frac{\mathrm{n}}{\mathrm{2}}}&\hline{\frac{\mathrm{n}}{\mathrm{2}}}&\hline{\frac{\mathrm{n}}{\mathrm{3}}}&\hline{\frac{\mathrm{n}}{\mathrm{3}}}\\\hline\end{array} \\ $$$$\mathrm{total}\:\mathrm{time}:\:\:\:\:\:\mathrm{2}\left(\frac{\mathrm{n}}{\mathrm{2}}\right)+\mathrm{2}\left(\frac{\mathrm{n}}{\mathrm{3}}\right)=\frac{\mathrm{5n}}{\mathrm{3}}=\mathrm{k}\: \\ $$$$ \\ $$$$\underline{\mathrm{In}\:\mathrm{2k}\:\mathrm{minutes}} \\ $$$$\mathrm{total}\:\mathrm{vegitables}: \\ $$$$\frac{\mathrm{5k}}{\mathrm{2}}+\mathrm{4n}=\mathrm{98} \\ $$$$\frac{\mathrm{5}}{\mathrm{2}}\centerdot\frac{\mathrm{5n}}{\mathrm{3}}+\mathrm{4n}=\mathrm{98}\:\:\:\left[\because\:\mathrm{k}=\frac{\mathrm{5n}}{\mathrm{3}}\right] \\ $$$$\frac{\mathrm{49n}}{\mathrm{6}}=\mathrm{98} \\ $$$$\:\:\:\:\:\mathrm{n}=\frac{\mathrm{98}×\mathrm{6}}{\mathrm{49}}=\mathrm{12} \\ $$

Commented by Tawa11 last updated on 05/Aug/22

God bless you sir. I appreciate.

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{appreciate}. \\ $$

Answered by Rasheed.Sindhi last updated on 05/Aug/22

Number of vegitables per minute determinant (((rad. ),(cucum.),(onions),(okra )),((46/t),(46/t),(69/t),(69/t))) Number of minutes per vegitable determinant (((rad. ),(cucum.),(onions),(okra )),((t/46),(t/46),(t/69),(t/69))) First k minutes k/4 minutes for each vegitable determinant ((,(rad. ),(cucu.),(onions),(okra )),((per min.),(46/t),(46/t),(69/t),(69/t)),((in (k/4) mins),((46k)/(4t)),((46k)/(4t)),((69k)/(4t)),((69k)/(4t)))) 2(((46k)/(4t)))+2(((69k)/(4t))) vegitables. Next k minutes n+n+n+n=4n vegitables time in each vegitable: determinant ((,(rad. ),(cucum.),(onions),(okra )),((per veg._(time) ),(t/46),(t/46),(t/69),(t/69)),((time in_(n vegs) ),((nt)/(46)),((nt)/(46)),((nt)/(69)),((nt)/(69)))) total time: 2(((nt)/(46)))+2(((nt)/(69)))=k In 2k minutes total vegitables: 2(((46k)/(4t)))+2(((69k)/(4t)))+4n=98 k(((46)/(2t))+((69)/(2t)))+4n=98 ∵ k=2(((nt)/(46)))+2(((nt)/(69))) from above. ∴ (2(((nt)/(46)))+2(((nt)/(69))))(((46)/(2t))+((69)/(2t)))+4n=98 t(2((n/(46)))+2((n/(69))))∙(1/t)(((46)/2)+((69)/2))+4n=98 ((n/(23))+((2n)/(69)))(((115)/2))+4n=98 (((25)/6)+4)n=98 ((49)/6)n=98 n=((98×6)/(49))=12

$$\underline{\mathrm{Number}\:\mathrm{of}\:\mathrm{vegitables}\:\mathrm{per}\:\mathrm{minute}} \\ $$$$\begin{array}{|c|c|}{\mathrm{rad}.\:\:\:\:}&\hline{\mathrm{cucum}.}&\hline{\mathrm{onions}}&\hline{\mathrm{okra}\:\:}\\{\mathrm{46}/\mathrm{t}}&\hline{\mathrm{46}/\mathrm{t}}&\hline{\mathrm{69}/\mathrm{t}}&\hline{\mathrm{69}/\mathrm{t}}\\\hline\end{array}\: \\ $$$$ \\ $$$$\underline{\mathrm{Number}\:\mathrm{of}\:\mathrm{minutes}\:\mathrm{per}\:\mathrm{vegitable}} \\ $$$$\begin{array}{|c|c|}{\mathrm{rad}.\:\:\:\:}&\hline{\mathrm{cucum}.}&\hline{\mathrm{onions}}&\hline{\mathrm{okra}\:\:}\\{\mathrm{t}/\mathrm{46}}&\hline{\mathrm{t}/\mathrm{46}}&\hline{\mathrm{t}/\mathrm{69}}&\hline{\mathrm{t}/\mathrm{69}}\\\hline\end{array}\: \\ $$$$ \\ $$$$\underline{\mathrm{First}\:\mathrm{k}\:\mathrm{minutes}} \\ $$$$\mathrm{k}/\mathrm{4}\:\mathrm{minutes}\:\mathrm{for}\:\mathrm{each}\:\mathrm{vegitable} \\ $$$$\begin{array}{|c|c|c|}{}&\hline{\mathrm{rad}.\:\:\:\:}&\hline{\mathrm{cucu}.}&\hline{\mathrm{onions}}&\hline{\mathrm{okra}\:\:}\\{\mathrm{per}\:\mathrm{min}.}&\hline{\mathrm{46}/\mathrm{t}}&\hline{\mathrm{46}/\mathrm{t}}&\hline{\mathrm{69}/\mathrm{t}}&\hline{\mathrm{69}/\mathrm{t}}\\{\mathrm{in}\:\frac{\mathrm{k}}{\mathrm{4}}\:\mathrm{mins}}&\hline{\frac{\mathrm{46k}}{\mathrm{4t}}}&\hline{\frac{\mathrm{46k}}{\mathrm{4t}}}&\hline{\frac{\mathrm{69k}}{\mathrm{4t}}}&\hline{\frac{\mathrm{69k}}{\mathrm{4t}}}\\\hline\end{array}\: \\ $$$$\mathrm{2}\left(\frac{\mathrm{46k}}{\mathrm{4t}}\right)+\mathrm{2}\left(\frac{\mathrm{69k}}{\mathrm{4t}}\right)\:\mathrm{vegitables}. \\ $$$$\underline{\mathrm{Next}\:\mathrm{k}\:\mathrm{minutes}} \\ $$$$\:\mathrm{n}+\mathrm{n}+\mathrm{n}+\mathrm{n}=\mathrm{4n}\:\mathrm{vegitables} \\ $$$$\:\mathrm{time}\:\mathrm{in}\:\mathrm{each}\:\mathrm{vegitable}: \\ $$$$\begin{array}{|c|c|c|}{}&\hline{\mathrm{rad}.\:\:\:\:}&\hline{\mathrm{cucum}.}&\hline{\mathrm{onions}}&\hline{\mathrm{okra}\:\:}\\{\underset{\mathrm{time}} {\mathrm{per}\:\mathrm{veg}.}}&\hline{\mathrm{t}/\mathrm{46}}&\hline{\mathrm{t}/\mathrm{46}}&\hline{\mathrm{t}/\mathrm{69}}&\hline{\mathrm{t}/\mathrm{69}}\\{\underset{\mathrm{n}\:\mathrm{vegs}} {\mathrm{time}\:\mathrm{in}}}&\hline{\frac{\mathrm{nt}}{\mathrm{46}}}&\hline{\frac{\mathrm{nt}}{\mathrm{46}}}&\hline{\frac{\mathrm{nt}}{\mathrm{69}}}&\hline{\frac{\mathrm{nt}}{\mathrm{69}}}\\\hline\end{array} \\ $$$$\mathrm{total}\:\mathrm{time}:\:\:\:\:\:\mathrm{2}\left(\frac{\mathrm{nt}}{\mathrm{46}}\right)+\mathrm{2}\left(\frac{\mathrm{nt}}{\mathrm{69}}\right)=\mathrm{k}\: \\ $$$$ \\ $$$$\underline{\mathrm{In}\:\mathrm{2k}\:\mathrm{minutes}} \\ $$$$\mathrm{total}\:\mathrm{vegitables}: \\ $$$$\mathrm{2}\left(\frac{\mathrm{46k}}{\mathrm{4t}}\right)+\mathrm{2}\left(\frac{\mathrm{69k}}{\mathrm{4t}}\right)+\mathrm{4n}=\mathrm{98} \\ $$$$\mathrm{k}\left(\frac{\mathrm{46}}{\mathrm{2t}}+\frac{\mathrm{69}}{\mathrm{2t}}\right)+\mathrm{4n}=\mathrm{98}\: \\ $$$$\because\:\:\mathrm{k}=\mathrm{2}\left(\frac{\mathrm{nt}}{\mathrm{46}}\right)+\mathrm{2}\left(\frac{\mathrm{nt}}{\mathrm{69}}\right)\:\mathrm{from}\:\mathrm{above}. \\ $$$$\therefore\:\:\left(\mathrm{2}\left(\frac{\mathrm{nt}}{\mathrm{46}}\right)+\mathrm{2}\left(\frac{\mathrm{nt}}{\mathrm{69}}\right)\right)\left(\frac{\mathrm{46}}{\mathrm{2t}}+\frac{\mathrm{69}}{\mathrm{2t}}\right)+\mathrm{4n}=\mathrm{98} \\ $$$$\cancel{\mathrm{t}}\left(\mathrm{2}\left(\frac{\mathrm{n}}{\mathrm{46}}\right)+\mathrm{2}\left(\frac{\mathrm{n}}{\mathrm{69}}\right)\right)\centerdot\frac{\mathrm{1}}{\cancel{\mathrm{t}}}\left(\frac{\mathrm{46}}{\mathrm{2}}+\frac{\mathrm{69}}{\mathrm{2}}\right)+\mathrm{4n}=\mathrm{98} \\ $$$$\left(\frac{\mathrm{n}}{\mathrm{23}}+\frac{\mathrm{2n}}{\mathrm{69}}\right)\left(\frac{\mathrm{115}}{\mathrm{2}}\right)+\mathrm{4n}=\mathrm{98} \\ $$$$\left(\frac{\mathrm{25}}{\mathrm{6}}+\mathrm{4}\right)\mathrm{n}=\mathrm{98} \\ $$$$\frac{\mathrm{49}}{\mathrm{6}}\mathrm{n}=\mathrm{98} \\ $$$$\mathrm{n}=\frac{\mathrm{98}×\mathrm{6}}{\mathrm{49}}=\mathrm{12} \\ $$

Commented by Tawa11 last updated on 05/Aug/22

Wow, God bless you sir

$$\mathrm{Wow},\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com