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Question-202566

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Question Number 202566 by MASANJAJJ last updated on 29/Dec/23
Answered by Rasheed.Sindhi last updated on 29/Dec/23
Selling price of one tshirt:7500+p where p>0 is profit per tshirt Let n tshirts are sold; n∈N Total sell=n(7500+p) Commission of Mr Tony: n(7500+p)×(9/(100))=297000 n(7500+p)=3300000 Only necessary restriction is that n is natural and p is +ve. For example p=1300⇒n=375 Many answers are possible.
$${Selling}\:{price}\:{of}\:{one}\:{tshirt}:\mathrm{7500}+{p} \\ $$$${where}\:{p}>\mathrm{0}\:{is}\:{profit}\:{per}\:{tshirt}\: \\ $$$${Let}\:{n}\:{tshirts}\:{are}\:{sold};\:{n}\in\mathbb{N} \\ $$$${Total}\:{sell}={n}\left(\mathrm{7500}+{p}\right) \\ $$$${Commission}\:{of}\:{Mr}\:{Tony}: \\ $$$${n}\left(\mathrm{7500}+{p}\right)×\frac{\mathrm{9}}{\mathrm{100}}=\mathrm{297000} \\ $$$${n}\left(\mathrm{7500}+{p}\right)=\mathrm{3300000} \\ $$$${Only}\:{necessary}\:{restriction}\:{is} \\ $$$${that}\:{n}\:{is}\:{natural}\:{and}\:{p}\:{is}\:+{ve}. \\ $$$${For}\:{example} \\ $$$${p}=\mathrm{1300}\Rightarrow{n}=\mathrm{375} \\ $$$${Many}\:{answers}\:{are}\:{possible}. \\ $$$$\: \\ $$
Commented by Rasheed.Sindhi last updated on 29/Dec/23
n(7500+p)=3300000 p=((3300000)/n)−7500<297000⇒n>11 =((440×7500−7500n)/n)=((7500(440−n))/n)⇒n<440 n∣7500 or n∣(440−n)⇒n∣440 n∣7500 or n∣440 We can calculate all possible values of n and therefore all corresponding values of p
$${n}\left(\mathrm{7500}+{p}\right)=\mathrm{3300000} \\ $$$${p}=\frac{\mathrm{3300000}}{{n}}−\mathrm{7500}<\mathrm{297000}\Rightarrow{n}>\mathrm{11} \\ $$$$\:\:\:=\frac{\mathrm{440}×\mathrm{7500}−\mathrm{7500}{n}}{{n}}=\frac{\mathrm{7500}\left(\mathrm{440}−{n}\right)}{{n}}\Rightarrow{n}<\mathrm{440} \\ $$$${n}\mid\mathrm{7500}\:\mathrm{or}\:\mathrm{n}\mid\left(\mathrm{440}−{n}\right)\Rightarrow{n}\mid\mathrm{440} \\ $$$${n}\mid\mathrm{7500}\:\mathrm{or}\:{n}\mid\mathrm{440} \\ $$$$ \\ $$$${We}\:{can}\:{calculate}\:{all}\:{possible}\:{values}\:{of}\:{n} \\ $$$${and}\:{therefore}\:{all}\:{corresponding}\:{values}\:{of}\:{p} \\ $$
Answered by mr W last updated on 29/Dec/23
for each T−shirt: 91% cost ≡ tsh 7500 9% commission ≡(9/(91))×7500≈742 tsh 297000 commission≡((297000)/(742)) ≈400 T−shirts ⇒Tony sold 400 T−shirts.
$${for}\:{each}\:{T}−{shirt}: \\ $$$$\mathrm{91\%}\:{cost}\:\equiv\:{tsh}\:\mathrm{7500} \\ $$$$\mathrm{9\%}\:{commission}\:\equiv\frac{\mathrm{9}}{\mathrm{91}}×\mathrm{7500}\approx\mathrm{742} \\ $$$${tsh}\:\mathrm{297000}\:{commission}\equiv\frac{\mathrm{297000}}{\mathrm{742}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\approx\mathrm{400}\:{T}−{shirts} \\ $$$$\Rightarrow{Tony}\:{sold}\:\mathrm{400}\:{T}−{shirts}. \\ $$
Commented by Rasheed.Sindhi last updated on 29/Dec/23
Sir, I didn′t think commission as profit. but i thought it as ′part of profit′.I thought Mr Tony a person who sells goods on behalf of an other person(original seller), because in my country commission is used in above sense. Anyway sir I′m not much confidant!
$$\mathrm{Sir},\:\mathrm{I}\:\mathrm{didn}'\mathrm{t}\:\mathrm{think}\:\mathrm{commission}\:\mathrm{as}\:{profit}. \\ $$$$\mathrm{but}\:\mathrm{i}\:\mathrm{thought}\:\mathrm{it}\:\mathrm{as}\:'\mathrm{part}\:\mathrm{of}\:\mathrm{profit}'.\mathrm{I}\:\mathrm{thought} \\ $$$$\mathrm{Mr}\:\mathrm{Tony}\:\mathrm{a}\:\mathrm{person}\:\mathrm{who}\:\mathrm{sells}\:\mathrm{goods}\:\mathrm{on}\:\mathrm{behalf} \\ $$$$\mathrm{of}\:\mathrm{an}\:\mathrm{other}\:\mathrm{person}\left(\mathrm{original}\:\mathrm{seller}\right),\:{because} \\ $$$${in}\:{my}\:{country}\:{commission}\:{is}\:{used}\:{in}\:{above} \\ $$$${sense}.\:{Anyway}\:\boldsymbol{{sir}}\:{I}'{m}\:{not}\:{much}\:{confidant}! \\ $$
Commented by mr W last updated on 29/Dec/23
I think the question only describes a simple situation as following. I don′t think Mr Tony has got a MBA degree. He is just a simple man who sales secondhand T−shirts on the market. He purchases each T−shirt for $7500 from a wholesaler and sales it for $8245 on the market. He earns $745 for each t−shirt he sold. He doesn′t care what we call his earning: if as profit or as commission.
$${I}\:{think}\:{the}\:{question}\:{only}\:{describes} \\ $$$${a}\:{simple}\:{situation}\:{as}\:{following}. \\ $$$${I}\:{don}'{t}\:{think}\:{Mr}\:{Tony}\:{has}\:{got}\:{a} \\ $$$${MBA}\:{degree}.\:\:{He}\:{is}\:{just}\:{a}\:{simple}\: \\ $$$${man}\:{who}\:{sales}\:{secondhand}\:{T}−{shirts} \\ $$$${on}\:{the}\:{market}.\:{He}\:{purchases}\:{each} \\ $$$${T}−{shirt}\:{for}\:\$\mathrm{7500}\:{from}\:{a}\: \\ $$$${wholesaler}\:{and}\:{sales}\:{it}\:{for}\:\$\mathrm{8245}\:{on}\: \\ $$$${the}\:{market}.\:{He}\:{earns}\:\$\mathrm{745}\:{for}\:{each} \\ $$$${t}−{shirt}\:{he}\:{sold}.\:{He}\:{doesn}'{t}\:{care} \\ $$$${what}\:{we}\:{call}\:{his}\:{earning}:\:{if}\:{as}\:{profit} \\ $$$${or}\:{as}\:{commission}. \\ $$
Commented by Rasheed.Sindhi last updated on 30/Dec/23
OK Sir,Thank you!
$$\mathcal{OK}\:\mathcal{S}{ir},\mathcal{T}{hank}\:{you}! \\ $$

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