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Question Number 7705 by Obenfo last updated on 10/Sep/16

A and B can do a work in 12 days and 17 days respectively and with the help of C they complete the work in 5 days and earn Rs. 238. Find the share of B.

$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{do}\:\mathrm{a}\:\mathrm{work}\:\mathrm{in}\:\mathrm{12}\:\mathrm{days}\:\mathrm{and} \\ $$$$\mathrm{17}\:\mathrm{days}\:\mathrm{respectively}\:\mathrm{and}\:\mathrm{with}\:\mathrm{the}\:\mathrm{help} \\ $$$$\mathrm{of}\:\mathrm{C}\:\mathrm{they}\:\mathrm{complete}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{5}\:\mathrm{days} \\ $$$$\mathrm{and}\:\mathrm{earn}\:\mathrm{Rs}.\:\mathrm{238}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{share}\:\mathrm{of}\:\mathrm{B}. \\ $$

Answered by Rasheed Soomro last updated on 10/Sep/16

A can do a work in 12 days In one day A can do (1/(12)) of whole work In 5 days A can do (5/(12)) of whole work B can do the work in 17 days In one day B can do (1/(17)) of whole work In 5 days B can do (5/(17)) of whole work In 5 days A,B & C can do the whole work Let C has done c of whole work (5/(12))+(5/(17))+c=1(whole work) c=1−(5/(12))−(5/(17))=((12×17−5×17−5×12)/(12×17))=((204−85−60)/(204))=((59)/(204)) In 5 days whole work A,B and C has respectively shared as follows (5/(12)) ,(5/(17)) ,((59)/(204)) So Rs 238 will be shared Share of A =238×(5/(12))=Rs 99(1/6) Share of B =238×(5/(17))=Rs 70 Share of A =238×((59)/(204))=Rs 68(5/6)

$${A}\:{can}\:{do}\:{a}\:{work}\:{in}\:\mathrm{12}\:{days} \\ $$$${In}\:{one}\:{day}\:{A}\:{can}\:{do}\:\frac{\mathrm{1}}{\mathrm{12}}\:{of}\:{whole}\:{work} \\ $$$${In}\:\mathrm{5}\:{days}\:{A}\:{can}\:{do}\:\:\:\frac{\mathrm{5}}{\mathrm{12}}\:{of}\:{whole}\:{work} \\ $$$${B}\:{can}\:{do}\:{the}\:{work}\:{in}\:\mathrm{17}\:{days} \\ $$$${In}\:{one}\:{day}\:{B}\:{can}\:{do}\:\frac{\mathrm{1}}{\mathrm{17}}\:{of}\:{whole}\:{work} \\ $$$${In}\:\:\mathrm{5}\:\:{days}\:{B}\:\:{can}\:{do}\:\:\frac{\mathrm{5}}{\mathrm{17}}\:{of}\:{whole}\:{work} \\ $$$${In}\:\mathrm{5}\:\:{days}\:{A},{B}\:\&\:{C}\:{can}\:{do}\:{the}\:{whole}\:{work} \\ $$$${Let}\:{C}\:{has}\:{done}\:{c}\:\:{of}\:{whole}\:{work} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{5}}{\mathrm{12}}+\frac{\mathrm{5}}{\mathrm{17}}+{c}=\mathrm{1}\left({whole}\:{work}\right) \\ $$$$\:\:\:\:\:\:{c}=\mathrm{1}−\frac{\mathrm{5}}{\mathrm{12}}−\frac{\mathrm{5}}{\mathrm{17}}=\frac{\mathrm{12}×\mathrm{17}−\mathrm{5}×\mathrm{17}−\mathrm{5}×\mathrm{12}}{\mathrm{12}×\mathrm{17}}=\frac{\mathrm{204}−\mathrm{85}−\mathrm{60}}{\mathrm{204}}=\frac{\mathrm{59}}{\mathrm{204}} \\ $$$${In}\:\mathrm{5}\:{days}\:{whole}\:{work}\:{A},{B}\:{and}\:{C}\:{has}\:{respectively}\:{shared}\:{as}\:{follows} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{5}}{\mathrm{12}}\:,\frac{\mathrm{5}}{\mathrm{17}}\:,\frac{\mathrm{59}}{\mathrm{204}} \\ $$$${So}\:{Rs}\:\mathrm{238}\:{will}\:{be}\:{shared} \\ $$$${Share}\:{of}\:{A}\:\:=\mathrm{238}×\frac{\mathrm{5}}{\mathrm{12}}={Rs}\:\mathrm{99}\frac{\mathrm{1}}{\mathrm{6}} \\ $$$${Share}\:{of}\:{B}\:\:=\mathrm{238}×\frac{\mathrm{5}}{\mathrm{17}}={Rs}\:\:\mathrm{70} \\ $$$${Share}\:{of}\:{A}\:\:=\mathrm{238}×\frac{\mathrm{59}}{\mathrm{204}}={Rs}\:\mathrm{68}\frac{\mathrm{5}}{\mathrm{6}} \\ $$$$ \\ $$

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