A-and-B-can-complete-a-piece-of-work-in-12-days-and-24-days-respectively-After-A-had-worked-for-6-days-B-joined-him-and-then-they-completed-the-work-How-much-should-A-receive-as-his-share-from-th

Question Number 95985 by mpym last updated on 29/May/20

$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{complete}\:\mathrm{a}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{work}\:\mathrm{in} \\ $$$$\mathrm{12}\:\mathrm{days}\:\mathrm{and}\:\mathrm{24}\:\mathrm{days}\:\mathrm{respectively}.\:\mathrm{After} \\ $$$$\mathrm{A}\:\mathrm{had}\:\mathrm{worked}\:\mathrm{for}\:\mathrm{6}\:\mathrm{days},\:\mathrm{B}\:\mathrm{joined}\:\mathrm{him}, \\ $$$$\mathrm{and}\:\mathrm{then}\:\mathrm{they}\:\mathrm{completed}\:\mathrm{the}\:\mathrm{work}.\:\mathrm{How} \\ $$$$\mathrm{much}\:\mathrm{should}\:\:\mathrm{A}\:\mathrm{receive}\:\mathrm{as}\:\mathrm{his}\:\mathrm{share}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{total}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{Rs}.\:\mathrm{180}\:\mathrm{paid}\:\mathrm{for} \\ $$$$\mathrm{completing}\:\mathrm{the}\:\mathrm{work}? \\ $$

Answered by mr W last updated on 29/May/20

$${A}\:{does}\:\frac{\mathrm{1}}{\mathrm{12}}\:{work}\:{each}\:{day} \\ $$$${B}\:{does}\:\frac{\mathrm{1}}{\mathrm{24}}\:{work}\:{each}\:{day} \\ $$$${A}\:{worked}\:\mathrm{6}\:{days}\:{alone},\:{then}\:{A}\:{and} \\ $$$${B}\:{work}\:{x}\:{days}\:{togother}: \\ $$$$\frac{\mathrm{6}+{x}}{\mathrm{12}}+\frac{{x}}{\mathrm{24}}=\mathrm{1} \\ $$$$\Rightarrow{x}=\mathrm{4} \\ $$$${total}\:{work}\:{done}\:{by}\:{A}:\:\frac{\mathrm{10}}{\mathrm{12}}=\frac{\mathrm{5}}{\mathrm{6}} \\ $$$${total}\:{work}\:{done}\:{by}\:{B}:\:\frac{\mathrm{4}}{\mathrm{24}}=\frac{\mathrm{1}}{\mathrm{6}} \\ $$$${A}\:{should}\:{get}\:\frac{\mathrm{5}}{\mathrm{6}}\:{of}\:{the}\:{total}\:{payment}, \\ $$$${i}.{e}.\:\frac{\mathrm{5}}{\mathrm{6}}×\mathrm{180}=\mathrm{150}\:{Rs} \\ $$$${B}\:{should}\:{get}\:\frac{\mathrm{1}}{\mathrm{6}}\:{of}\:{the}\:{total}\:{payment}, \\ $$$${i}.{e}.\:\frac{\mathrm{1}}{\mathrm{6}}×\mathrm{180}=\mathrm{30}\:{Rs} \\ $$

Commented by mr W last updated on 29/May/20

$${this}\:{is}\:{the}\:{result}\:{in}\:{mathematics}. \\ $$$$ \\ $$$${now}\:{the}\:{result}\:{in}\:{practice}: \\ $$$${A}\:{gets}\:\mathrm{30}\:{Rs}\:{and}\:{B}\:{gets}\:\mathrm{150}\:{Rs},\:{since} \\ $$$${B}\:{is}\:{the}\:{nephew}\:{of}\:{the}\:{boss}. \\ $$

Commented by bobhans last updated on 29/May/20

can C get everything, because C is a thug

Commented by i jagooll last updated on 29/May/20

$$\mathrm{hahahahaha} \\ $$

Commented by som(math1967) last updated on 29/May/20

$$\mathrm{Haha} \\ $$

Commented by john santu last updated on 29/May/20

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Answered by som(math1967) last updated on 29/May/20

$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{work}\:\mathrm{together}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{day}\:\:=\frac{\mathrm{1}}{\mathrm{12}}\:+\frac{\mathrm{1}}{\mathrm{24}}=\frac{\mathrm{1}}{\mathrm{8}}\:\mathrm{part}\:\mathrm{of}\:\mathrm{work} \\ $$$$\mathrm{In}\:\mathrm{6day}\:\mathrm{A}\:\mathrm{complete}=\frac{\mathrm{6}}{\mathrm{12}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{A},\mathrm{B}\:\mathrm{complete}\:=\mathrm{8}×\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{4days} \\ $$$$\mathrm{A}'\mathrm{s}\:\mathrm{work}:\mathrm{B}'\mathrm{s}\:\mathrm{work} \\ $$$$=\mathrm{10}×\frac{\mathrm{1}}{\mathrm{12}}:\mathrm{4}×\frac{\mathrm{1}}{\mathrm{24}} \\ $$$$=\frac{\mathrm{5}}{\mathrm{6}}:\frac{\mathrm{1}}{\mathrm{6}}=\mathrm{5}:\mathrm{1}\therefore \\ $$$$\therefore\mathrm{A}'\mathrm{s}\:\mathrm{share}=\frac{\mathrm{5}}{\mathrm{6}}×\mathrm{180}=\mathrm{Rs150} \\ $$

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