SSC GD Constable 4 Feb 2025 Shift 3 Paper

Speed of boat in still water $=\frac{\text{ Downstreamspeed } + \text{ Upstreamspeed }}{2}$Downstream speed = Speed of boat in still water + Speed of the streamUpstream speed $=$ Speed of boat in still water - Speed of the streamCalculation:Let the speed of the boat in still water be $x\text{ km/h}$.Downstream speed $= x + 9\text{ km/h}$Upstream speed $= x - 9\text{ km/h}$Time taken to travel downstream $=\frac{56}{x+9}$Time taken to travel upstream $=28$ / ( $x-9$ )Total time $=7$ hours$\Rightarrow \frac{56}{x+9} + \frac{28}{x-9} = 7$Multiply both sides by $(x+9)(x-9)$ :$\; \Rightarrow 56(x-9) + 28(x+9) = 7(x+9)(x-9)$$\; \Rightarrow 56x - 504 + 28x + 252 = 7(x^2 - 81)$$\; \Rightarrow 84x - 252 = 7x^2 - 567$Rearrange the equation:$\Rightarrow 7x^2 - 84x - 315 = 0$Divide the entire equation by 7 :$\Rightarrow x^2 - 12x - 45 = 0$ Factorize the quadratic equation:$\; \Rightarrow (x-15)(x+3) = 0$$\; \Rightarrow x=15 \; \text{ or } \; x=-3$Since speed cannot be negative, $x=15\text{ km/h}$.