Question Number 6786 by Rasheed Soomro last updated on 25/Jul/16
$${Three}\:{Arabs}\:{A},{B}\:{and}\:{C}\:{were}\:{traveling} \\ $$$${together}.\:{On}\:{the}\:{lunch}\:{time}\:{A}\:{and}\:\:{B} \\ $$$${produce}\:{m}\:{and}\:\:{n}\:{loaves}\:{of}\:{bread}\:{respectively} \\ $$$${for}\:{eating}\:{but}\:{C}\:{have}\:{no}\:{loaf}\:{of}\:{bread}.\:{All} \\ $$$${the}\:{three}\:{ate}\:{together}.\:\:{After}\:{completing} \\ $$$${lunch}\:{C}\:\:{gave}\:{A}\:{and}\:{B}\:{m}+{n}\:{darhams}. \\ $$$${How}\:{shoud}\:{they}\:{divide}\:{this}\:{sum}? \\ $$$$ \\ $$
Commented by prakash jain last updated on 25/Jul/16
$$\mathrm{Assuming}\:\mathrm{all}\:\mathrm{three}\:\mathrm{consumed}\:\mathrm{equally}\:\frac{{m}+{n}}{\mathrm{3}} \\ $$$$\mathrm{A}\:\mathrm{contributed}={m}−\frac{{m}+{n}}{\mathrm{3}}=\frac{\mathrm{2}{m}−{n}}{\mathrm{3}} \\ $$$$\mathrm{B}\:\mathrm{contributed}={n}−\frac{{n}+{m}}{\mathrm{3}}=\frac{\mathrm{2}{n}−{m}}{\mathrm{3}} \\ $$$$\mathrm{Since}\:\mathrm{A}\:\mathrm{and}\:\mathrm{Bdid}\:\mathrm{not}\:\mathrm{pay}\:\mathrm{anything}\:\mathrm{we}\:\mathrm{assume} \\ $$$${m}\geqslant\frac{{m}+{n}}{\mathrm{3}}\:\mathrm{and}\:{n}\geqslant\frac{{n}+{m}}{\mathrm{3}} \\ $$$$\mathrm{C}\:\mathrm{paid}\:\left({m}+{n}\right)\:\mathrm{for}\:\frac{{m}+{n}}{\mathrm{3}}\:\mathrm{so}\:\mathrm{one}\:\mathrm{bread}\:\mathrm{cost}=\mathrm{3} \\ $$$$\mathrm{A}\:\mathrm{will}\:\mathrm{get}=\mathrm{2}{m}−{n} \\ $$$$\mathrm{B}\:\mathrm{will}\:\mathrm{get}=\mathrm{2}{n}−{m} \\ $$
Commented by Rasheed Soomro last updated on 26/Jul/16
$$\mathcal{G}{ood}\:\mathcal{E}{xplanation}! \\ $$