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Question Number 6743 by Tawakalitu. last updated on 20/Jul/16

P and Q are partners in a venture,  P  contributed #20,000 for  nine month, and Q contributed #50,000 for one year. find each  person share of  profit of #6,300

$${P}\:{and}\:{Q}\:{are}\:{partners}\:{in}\:{a}\:{venture},\:\:{P}\:\:{contributed}\:#\mathrm{20},\mathrm{000}\:{for} \\ $$$${nine}\:{month},\:{and}\:{Q}\:{contributed}\:#\mathrm{50},\mathrm{000}\:{for}\:{one}\:{year}.\:{find}\:{each} \\ $$$${person}\:{share}\:{of}\:\:{profit}\:{of}\:#\mathrm{6},\mathrm{300} \\ $$$$ \\ $$

Answered by Rasheed Soomro last updated on 20/Jul/16

In order to compare the investments of   P   and   Q   and then divide the profit in  light of that coparison we need to determine  the investments for same period.  An easy way is to determine for one month.    Contribution of  #20,000  for  9 months                               =Contribution  #(9×20,000) for 1 month.                               =#180,000 for  1  month.    Contribution of  #50,000 for  12 months                                 =Contribution #(12×50,000) for 1 month                                 =#600,000 for 1 month.    Ratio of investments of P   and  Q                                   =#180,000:#600,000=18:60=3:10                              profit of P= 6300×(3/(13))≈1453.85                              profit of Q= 6300×((10)/(13))≈4846.15

$${In}\:{order}\:{to}\:{compare}\:{the}\:{investments}\:{of}\: \\ $$$${P}\:\:\:{and}\:\:\:{Q}\:\:\:{and}\:{then}\:{divide}\:{the}\:{profit}\:{in} \\ $$$${light}\:{of}\:{that}\:{coparison}\:{we}\:{need}\:{to}\:{determine} \\ $$$${the}\:{investments}\:{for}\:\boldsymbol{{same}}\:\boldsymbol{{period}}. \\ $$$${An}\:{easy}\:{way}\:{is}\:{to}\:{determine}\:{for}\:\boldsymbol{{one}}\:\boldsymbol{{month}}. \\ $$$$ \\ $$$${Contribution}\:{of}\:\:#\mathrm{20},\mathrm{000}\:\:{for}\:\:\mathrm{9}\:{months} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={Contribution}\:\:#\left(\mathrm{9}×\mathrm{20},\mathrm{000}\right)\:{for}\:\mathrm{1}\:{month}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=#\mathrm{180},\mathrm{000}\:{for}\:\:\mathrm{1}\:\:{month}. \\ $$$$ \\ $$$${Contribution}\:{of}\:\:#\mathrm{50},\mathrm{000}\:{for}\:\:\mathrm{12}\:{months} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={Contribution}\:#\left(\mathrm{12}×\mathrm{50},\mathrm{000}\right)\:{for}\:\mathrm{1}\:{month} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=#\mathrm{600},\mathrm{000}\:{for}\:\mathrm{1}\:{month}. \\ $$$$ \\ $$$${Ratio}\:{of}\:{investments}\:{of}\:{P}\:\:\:{and}\:\:{Q} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=#\mathrm{180},\mathrm{000}:#\mathrm{600},\mathrm{000}=\mathrm{18}:\mathrm{60}=\mathrm{3}:\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{profit}\:{of}\:{P}=\:\mathrm{6300}×\frac{\mathrm{3}}{\mathrm{13}}\approx\mathrm{1453}.\mathrm{85} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{profit}\:{of}\:{Q}=\:\mathrm{6300}×\frac{\mathrm{10}}{\mathrm{13}}\approx\mathrm{4846}.\mathrm{15} \\ $$$$\:\:\:\:\:\:\: \\ $$

Commented by Tawakalitu. last updated on 20/Jul/16

Thanks so much

$${Thanks}\:{so}\:{much} \\ $$

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