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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?

$${Three}\:{Arabs}\:{A},{B}\:{and}\:{C}\:{were}\:{traveling} \\ $$$${together}.\:{On}\:{the}\:{lunch}\:{time}\:{A}\:{and}\:\:{B} \\ $$$${produce}\:{m}\:{and}\:\:{n}\:{loaves}\:{of}\:{bread}\:{respectively} \\ $$$${for}\:{eating}\:{but}\:{C}\:{have}\:{no}\:{loaf}\:{of}\:{bread}.\:{All} \\ $$$${the}\:{three}\:{ate}\:{together}.\:\:{After}\:{completing} \\ $$$${lunch}\:{C}\:\:{gave}\:{A}\:{and}\:{B}\:{m}+{n}\:{darhams}. \\ $$$${How}\:{shoud}\:{they}\:{divide}\:{this}\:{sum}? \\ $$$$ \\ $$

Commented by prakash jain last updated on 25/Jul/16

Assuming all three consumed equally ((m+n)/3)  A contributed=m−((m+n)/3)=((2m−n)/3)  B contributed=n−((n+m)/3)=((2n−m)/3)  Since A and Bdid not pay anything we assume  m≥((m+n)/3) and n≥((n+m)/3)  C paid (m+n) for ((m+n)/3) so one bread cost=3  A will get=2m−n  B will get=2n−m

$$\mathrm{Assuming}\:\mathrm{all}\:\mathrm{three}\:\mathrm{consumed}\:\mathrm{equally}\:\frac{{m}+{n}}{\mathrm{3}} \\ $$$$\mathrm{A}\:\mathrm{contributed}={m}−\frac{{m}+{n}}{\mathrm{3}}=\frac{\mathrm{2}{m}−{n}}{\mathrm{3}} \\ $$$$\mathrm{B}\:\mathrm{contributed}={n}−\frac{{n}+{m}}{\mathrm{3}}=\frac{\mathrm{2}{n}−{m}}{\mathrm{3}} \\ $$$$\mathrm{Since}\:\mathrm{A}\:\mathrm{and}\:\mathrm{Bdid}\:\mathrm{not}\:\mathrm{pay}\:\mathrm{anything}\:\mathrm{we}\:\mathrm{assume} \\ $$$${m}\geqslant\frac{{m}+{n}}{\mathrm{3}}\:\mathrm{and}\:{n}\geqslant\frac{{n}+{m}}{\mathrm{3}} \\ $$$$\mathrm{C}\:\mathrm{paid}\:\left({m}+{n}\right)\:\mathrm{for}\:\frac{{m}+{n}}{\mathrm{3}}\:\mathrm{so}\:\mathrm{one}\:\mathrm{bread}\:\mathrm{cost}=\mathrm{3} \\ $$$$\mathrm{A}\:\mathrm{will}\:\mathrm{get}=\mathrm{2}{m}−{n} \\ $$$$\mathrm{B}\:\mathrm{will}\:\mathrm{get}=\mathrm{2}{n}−{m} \\ $$

Commented by Rasheed Soomro last updated on 26/Jul/16

Good Explanation!

$$\mathcal{G}{ood}\:\mathcal{E}{xplanation}! \\ $$

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