Question Number 211617 by pete last updated on 14/Sep/24
$$\mathrm{Ato}\:\:\mathrm{starts}\:\mathrm{a}\:\mathrm{business}\:\mathrm{with}\:\$\mathrm{1},\mathrm{250}.\mathrm{00}.\:\mathrm{Ama}\:\mathrm{joins}\:\mathrm{the}\:\mathrm{business} \\ $$$$\mathrm{later}\:\mathrm{with}\:\mathrm{a}\:\mathrm{capital}\:\mathrm{of}\:\mathrm{1},\mathrm{875}.\mathrm{00}.\:\mathrm{At}\:\mathrm{the}\: \\ $$$$\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{year},\:\mathrm{profits}\:\mathrm{are}\:\mathrm{shared}\:\mathrm{equally} \\ $$$$\mathrm{between}\:\mathrm{Ato}\:\mathrm{and}\:\mathrm{Ama}.\:\mathrm{When}\:\mathrm{did}\:\mathrm{Ama} \\ $$$$\mathrm{join}\:\mathrm{the}\:\mathrm{business}? \\ $$
Answered by A5T last updated on 14/Sep/24
$${Let}\:{x}\:{be}\:{the}\:{average}\:{monthly}\:{profit}\left({in}\:\%\:{of}\:\right. \\ $$$$\left.{capital}\right).\:{If}\:{it}\:{is}\:{the}\:{same}\:{for}\:{both}\:{Ato}\:{and}\:{Ama} \\ $$$${Then}\:{Ato}'{s}\:{profit}\:{is}\:\mathrm{12}{x}×\mathrm{1250};\: \\ $$$${and}\:{Ama}'{s}\:{profit}={kx}×\mathrm{1875} \\ $$$$\left({where}\:{k}\:{is}\:{the}\:{number}\:{of}\:{months}\:{Ama}\:{used}\right) \\ $$$$\mathrm{12}{x}×\mathrm{1250}={kx}×\mathrm{1875}\Rightarrow{k}=\mathrm{8} \\ $$$$\Rightarrow{Ama}\:{joined}\:{the}\:{business}\:{after}\:{the}\:\mathrm{12}−\mathrm{8}=\mathrm{4}{th} \\ $$$${month}. \\ $$
Commented by pete last updated on 15/Sep/24
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{sir} \\ $$