A) \[\text{67}\frac{1}{5}days\]
B) \[\text{65}\frac{2}{5}days\]
C) \[\text{67}\frac{3}{5}days\]
D) \[\text{65}\frac{1}{5}days\]
E) None of these
Correct Answer: A
Solution :
\[\text{3}\times \]Raju's daily work = (Suinan + Vinit)'s daily work \[4\times \]Raju's daily work = (Raju + Suman + Vinit)'s daily work \[=\frac{1}{28}\] \[\therefore \] Raju's daily work \[=\frac{1}{28\times 4}=\frac{1}{112}\] Again, \[2\times \]Vinit's daily work = (Raju + Suman)'s daily work \[3\times \] Vinit's daily work = (Raju+Suman+Vinit)'s daily work\[=\frac{1}{28}\] \[\therefore \]Vinit?s daily work \[=\frac{1}{28\times 3}=\frac{1}{84}\] Suman's daily work \[=\frac{1}{28}-\left( \frac{1}{112}+\frac{1}{84} \right)=\frac{4-1+3}{112}\] \[=\frac{12-(3+4)}{336}=\frac{5}{336}\] Hence Suman can finish the work in \[\frac{336}{5}days,\,\,ie\,\,67\frac{1}{5}days\] Quicker Method: Ration of efficiencies: \[\text{R : S + V = 1 : 3}...\text{(1)}\] \[\text{V : R + S = 1 : 2}...(2)\] \[(1)\times 3\](Sum of terms of equation (2) And \[(2)\times 4\] (Sum of ratio terms of equation (1)) \[\Rightarrow R:S+V=3:9\] \[V:R+S=4:8\] \[\Rightarrow R:V:S=3:4:5\] \[(\because S=9-4=5)\] Now, R+V:S with 3+4+5=12 efficiencies they do work in 28 days. \[\Rightarrow \] With I efficiency work can be done in \[28\times 12\] days \[\therefore \] Suman with 5 efficiency can do it in. \[\frac{28\times 12}{5}=\frac{336}{5}=67\frac{1}{5}days\]
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