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Question Number 215755 by Davidtim last updated on 17/Jan/25

Tow men complet a work in 3hr, three women complet it in 5hr, and five children complet it in 10hr. if we consider among these one man, one woman and one child in how much time they will complet it together?

$${Tow}\:{men}\:{complet}\:{a}\:{work}\:{in}\:\mathrm{3}{hr},\:{three} \\ $$$${women}\:{complet}\:{it}\:{in}\:\mathrm{5}{hr},\:{and}\:{five}\: \\ $$$${children}\:{complet}\:{it}\:{in}\:\mathrm{10}{hr}.\:{if}\:{we}\:{consider} \\ $$$${among}\:{these}\:{one}\:{man},\:{one}\:{woman}\:{and}\:{one} \\ $$$${child}\:{in}\:{how}\:{much}\:{time}\:{they}\:{will} \\ $$$${complet}\:{it}\:{together}? \\ $$

Answered by A5T last updated on 17/Jan/25

One man completes (1/(2×3))=(1/6) of the work in 1hr One woman completes (1/(3×5))=(1/(15)) of the work in 1hr One child completes (1/(5×10))=(1/(50)) of the work in 1hr ⇒ One man, one woman and one child will complete (1/6)+(1/(15))+(1/(50))=((19)/(75)) of the work in 1hr ⇒They complete in work in ((75)/(19))hrs=3((18)/(19))hrs

$$\mathrm{One}\:\mathrm{man}\:\mathrm{completes}\:\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{6}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{1hr} \\ $$$$\mathrm{One}\:\mathrm{woman}\:\mathrm{completes}\:\frac{\mathrm{1}}{\mathrm{3}×\mathrm{5}}=\frac{\mathrm{1}}{\mathrm{15}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{1hr} \\ $$$$\mathrm{One}\:\mathrm{child}\:\mathrm{completes}\:\frac{\mathrm{1}}{\mathrm{5}×\mathrm{10}}=\frac{\mathrm{1}}{\mathrm{50}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{1hr} \\ $$$$\Rightarrow\:\mathrm{One}\:\mathrm{man},\:\mathrm{one}\:\mathrm{woman}\:\mathrm{and}\:\mathrm{one}\:\mathrm{child}\:\mathrm{will} \\ $$$$\mathrm{complete}\:\frac{\mathrm{1}}{\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{15}}+\frac{\mathrm{1}}{\mathrm{50}}=\frac{\mathrm{19}}{\mathrm{75}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{1hr} \\ $$$$\Rightarrow\mathrm{They}\:\mathrm{complete}\:\mathrm{in}\:\mathrm{work}\:\mathrm{in}\:\frac{\mathrm{75}}{\mathrm{19}}\mathrm{hrs}=\mathrm{3}\frac{\mathrm{18}}{\mathrm{19}}\mathrm{hrs} \\ $$

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