A) \[A-(iv);\,B-(iii);\,C-(ii);\,D-(i)\]
B) \[A-(iii);\,B-(iv);\,C-(ii);\,D-(i)\]
C) \[A-(iii);\,B-(iv);\,C-(i);\,D-(ii)\]
D) \[A-(iv);\,B-(iii);\,C-(i);\,D-(ii)\]
Correct Answer: B
Solution :
\[x\times \frac{5}{4}\,-x\times \frac{5}{14}=25\Rightarrow \,\frac{25x}{28}=25\Rightarrow x=28\] where ?x? is required number A?s hare \[=\frac{3}{16}x,\,B's\] \[=\frac{x}{4}\] and C?s share \[=x-\left( \frac{3}{16}x+\frac{x}{4} \right)=\frac{9}{16}x\] where x= total amount. Now, \[\frac{9x}{16}=81\Rightarrow \,x=144\] \[\therefore \] B?s share \[=144\times \frac{1}{4}\,=36\] Money spent \[=\frac{5}{6}\] Remaining money \[=1-\frac{5}{6}\,=\frac{1}{6}\] Money earned \[=\frac{1}{12}\] Total money with him \[=\frac{1}{6}\,+\frac{1}{12}\,=\frac{1}{4}\] \[\frac{1}{8}\text{th}\] part of pencil = black. \[\Rightarrow \] Remaining part of pencil \[=1-\frac{7}{8}\,=\frac{7}{8}\] Yellow part \[=\frac{1}{2}\times \frac{7}{8}\,=\frac{7}{16}\] Blue part \[=1-\left( \frac{1}{8}-\frac{7}{16} \right)=\frac{7}{16}\] But given blue part = 3.5 cm \[\therefore \]Total length \[=3.5\times \frac{16}{7}\,=8\,cm\]
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