SSC CGL 6 Sep 2016 Paper

In ΔPST and ΔPQR,
∠ PST = ∠ PQR (Since ST || QR)
∠ PTS = ∠ PRQ
∴ By AA– similarity,
Δ PST ~ Δ PQR
∴ $\frac{\mathit{P}\mathit{S}}{\mathit{P}\mathit{Q}}$ = $\frac{\mathit{P}\mathit{T}}{\mathit{P}\mathit{R}}$
⇒ $\frac{\mathit{P}\mathit{Q}}{\mathit{P}\mathit{S}}$ = $\frac{\mathit{P}\mathit{R}}{\mathit{P}\mathit{T}}$
⇒ $\frac{\mathit{P}\mathit{S}+\mathit{S}\mathit{Q}}{\mathit{P}\mathit{S}}$ = $\frac{6}{\mathit{P}\mathit{T}}$
⇒ 1 + $\frac{\mathit{S}\mathit{Q}}{\mathit{P}\mathit{S}}$ = $\frac{6}{\mathit{P}\mathit{T}}$
⇒ 1 + $\frac{5}{3}$ = $\frac{6}{\mathit{P}\mathit{T}}$
⇒ $\frac{8}{3}$ = $\frac{6}{\mathit{P}\mathit{T}}$
⇒ 8 PT = 6 × 3
⇒ PT = $\frac{6\times 3}{8}$ = $\frac{9}{4}$ = 2.25 cm.