Question Number 25667 by adityapratap2585@gmail.com last updated on 12/Dec/17
$$\mathrm{Deepak}\:\mathrm{srarts}\:\mathrm{a}\:\mathrm{work}\:\mathrm{and}\:\mathrm{work}\:\mathrm{for}\:\mathrm{12} \\ $$$$\mathrm{days}\:\mathrm{and}\:\mathrm{find}\:\mathrm{he}\:\mathrm{has}\:\mathrm{ompleted}\:\mathrm{10\%}\: \\ $$$$\mathrm{less}\:\mathrm{work}\:\mathrm{which}\:\mathrm{he}\:\mathrm{had}\:\mathrm{to}\:\mathrm{finish}\:\mathrm{in}\: \\ $$$$\mathrm{order}\:\mathrm{to}\:\mathrm{complete}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{24}\:\mathrm{days}\bar {,} \\ $$$$\mathrm{so}\:\mathrm{he}\:\mathrm{ask}\:\mathrm{Rahman}\:\mathrm{to}\:\mathrm{join}\:\mathrm{him}\:\mathrm{to}\:\mathrm{finish} \\ $$$$\mathrm{the}\:\mathrm{work}\:\mathrm{on}\:\mathrm{time}\:.\:\mathrm{If}\:\mathrm{Rahman}\:\mathrm{work}\: \\ $$$$\mathrm{half}\:\mathrm{day}\:\mathrm{only}\:\mathrm{for}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{days}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{efficiency}\:\mathrm{of}\:\mathrm{Rahman}\:\mathrm{is}\:\mathrm{what} \\ $$$$\mathrm{percent}\:\mathrm{less}\:\mathrm{then}\:\mathrm{the}\:\mathrm{efficiency}\:\mathrm{of} \\ $$$$\mathrm{Deepak}\:? \\ $$
Commented by Rasheed.Sindhi last updated on 14/Dec/17
![Contribution of Deepak in work 90% Contribution of Rahman in work 10% Deepak, in 24 days contributes (9/(10)) of work Rahman, in 6 days contributes (1/(10)) of work [12 half days=6 days (full)] In one day : Deepak contributes (9/(10×24))=(3/(80)) of work. Rahman contributes (1/(10×6))=(1/(60)) of work. (3/(80))−(1/(60))=(1/(48)) (1/(48))=(x/(100))⇒x=((100)/(48))=((25)/(12)) So Rahman has ((25)/(12))%less efficiency](https://www.tinkutara.com/question/Q25766.png)
$$\mathrm{Contribution}\:\mathrm{of}\:\mathrm{Deepak}\:\mathrm{in}\:\mathrm{work}\:\:\mathrm{90\%} \\ $$$$\mathrm{Contribution}\:\mathrm{of}\:\mathrm{Rahman}\:\mathrm{in}\:\mathrm{work}\:\:\mathrm{10\%} \\ $$$$\mathrm{Deepak}, \\ $$$$\:\:\mathrm{in}\:\mathrm{24}\:\mathrm{days}\:\mathrm{contributes}\:\frac{\mathrm{9}}{\mathrm{10}}\:\mathrm{of}\:\mathrm{work} \\ $$$$\mathrm{Rahman}, \\ $$$$\:\:\mathrm{in}\:\mathrm{6}\:\mathrm{days}\:\mathrm{contributes}\:\frac{\mathrm{1}}{\mathrm{10}}\:\mathrm{of}\:\mathrm{work} \\ $$$$\:\:\:\:\:\:\:\left[\mathrm{12}\:\mathrm{half}\:\mathrm{days}=\mathrm{6}\:\mathrm{days}\:\left(\mathrm{full}\right)\right] \\ $$$$\mathrm{In}\:\mathrm{one}\:\mathrm{day}\:: \\ $$$$\mathrm{Deepak}\:\mathrm{contributes}\:\frac{\mathrm{9}}{\mathrm{10}×\mathrm{24}}=\frac{\mathrm{3}}{\mathrm{80}}\:\mathrm{of}\:\mathrm{work}. \\ $$$$\mathrm{Rahman}\:\mathrm{contributes}\:\frac{\mathrm{1}}{\mathrm{10}×\mathrm{6}}=\frac{\mathrm{1}}{\mathrm{60}}\:\mathrm{of}\:\mathrm{work}. \\ $$$$\:\:\frac{\mathrm{3}}{\mathrm{80}}−\frac{\mathrm{1}}{\mathrm{60}}=\frac{\mathrm{1}}{\mathrm{48}} \\ $$$$\frac{\mathrm{1}}{\mathrm{48}}=\frac{\mathrm{x}}{\mathrm{100}}\Rightarrow\mathrm{x}=\frac{\mathrm{100}}{\mathrm{48}}=\frac{\mathrm{25}}{\mathrm{12}} \\ $$$$\mathrm{So}\:\mathrm{Rahman}\:\mathrm{has}\:\frac{\mathrm{25}}{\mathrm{12}}\%\mathrm{less}\:\mathrm{efficiency} \\ $$
Commented by Rasheed.Sindhi last updated on 14/Dec/17
$$\mathrm{Please}\:\mathrm{confirm}\:\mathrm{the}\:\mathrm{answer}. \\ $$