SSC संयुक्त स्नातक स्तरीय टीयर-1 प्रैक्टिस सेट 1

प्रश्नानुसार,$\frac{\mathit{A}\mathit{O}}{\mathit{O}\mathit{E}}=\frac{5}{4}$ तथा $\frac{\mathit{C}\mathit{O}}{\mathit{O}\mathit{D}}=\frac{3}{2}$
$\mathrm{\Delta }\mathit{A}\mathit{B}\mathit{E}$ में, $\frac{\mathit{A}\mathit{B}}{\mathit{B}\mathit{E}}=\frac{\mathit{A}\mathit{O}}{\mathit{O}\mathit{E}}=\frac{5}{4}$
$\mathrm{\Delta }\mathit{A}\mathit{E}\mathit{C}$ में, $\frac{\mathit{A}\mathit{C}}{\mathit{C}\mathit{E}}=\frac{\mathit{A}\mathit{O}}{\mathit{O}\mathit{E}}=\frac{5}{4}$
$\mathrm{\Delta }\mathit{C}\mathit{D}\mathit{A}$ में, $\frac{\mathit{A}\mathit{C}}{\mathit{A}\mathit{D}}=\frac{\mathit{C}\mathit{O}}{\mathit{O}\mathit{D}}=\frac{3}{2}$
$\mathrm{\Delta }\mathit{C}\mathit{D}\mathit{B}$ में, $\frac{\mathit{B}\mathit{C}}{\mathit{B}\mathit{D}}=\frac{\mathit{C}\mathit{O}}{\mathit{O}\mathit{D}}=\frac{3}{2}$
$\therefore \mathit{A}\mathit{B}=5\mathit{x}=2\mathit{w}+2\mathit{z}$
$\Rightarrow 4\mathit{x}+4\mathit{y}=3\mathit{w}$ ........(i)
$\Rightarrow 2\mathit{w}+2\mathit{z}=5\mathit{x}$ .........(ii)
$\left(\because 5\mathit{y}=3\mathit{z}\Rightarrow \mathit{z}=\frac{5}{3}\mathit{y}\right)$
$\Rightarrow 2\mathit{w}+2\times \frac{5}{3}\mathit{y}=5\mathit{x}$
$\Rightarrow 6\mathit{w}+10\mathit{y}=15\mathit{x}$
$\therefore 6\mathit{w}=15\mathit{x}-10\mathit{y}\mathrm{}$ .......(iii)
समी (i) में 2 से गुणा करने पर,
$8\mathit{x}+8\mathit{y}=6\mathit{w}$
.........(iv)
समी (iii) व (iv) से,
$15\mathit{x}-10\mathit{y}=8\mathit{x}+8\mathit{y}$
$\Rightarrow 7\mathit{x}=18\mathit{y}$
$\therefore \mathit{y}=\frac{7}{18}\mathit{x}$
$\mathit{y}$ का मान समी (i) में रखने पर,
$4\mathit{x}+4\times \frac{7}{18}\mathit{x}=3\mathit{w}$
$\Rightarrow \frac{36\mathit{x}+14\mathit{x}}{9}$
$\Rightarrow 3\mathit{w}=\frac{50}{9}\mathit{x}$
$\therefore \mathit{A}\mathit{B}=5\mathit{x},\mathit{B}\mathit{C}=3\mathit{w}=\frac{50}{9}\mathit{x}$
$\therefore \frac{\mathit{A}\mathit{F}}{\mathit{F}\mathit{C}}=\frac{\mathit{A}\mathit{B}}{\mathit{B}\mathit{C}}$ $=\frac{5\mathit{x}}{\frac{50}{9}\mathit{x}}=\frac{9}{10}$
$\therefore \mathit{A}\mathit{F}=\frac{9}{19}\mathit{A}\mathit{C}=\frac{9}{19}\times 5\mathit{y}$
$=\frac{9}{19}\times 5\times \frac{7}{18}\mathit{x}=\frac{35}{38}\mathit{x}$
$\therefore \frac{\mathit{B}\mathit{O}}{\mathit{O}\mathit{F}}=\frac{\mathit{A}\mathit{B}}{\mathit{A}\mathit{F}}=\frac{5\mathit{x}}{\frac{35}{38}\mathit{x}}$ $=\frac{38\times 5}{35}=\frac{38}{7}$