RRB Assistant Loco Pilot and Technician Model Paper 1 with solutions

(a) Speed of ship = 30 kmph
= $\frac{30\times 5}{18}$ m / sec = $\frac{25}{3}$ m / sec.
Time taken in covering 500 metre
= $\frac{500\times 3}{25}$ = 60 seconds
Speed of radio waves
= $\frac{200}{1000}$ km / sec = $\frac{1}{5}$ km / sec.

∴ $\frac{\sqrt{{\mathit{x}}^2+\frac{1}{4}}}{\frac{1}{5}}+\frac{\mathit{x}}{\frac{1}{5}}$ = 60
⇒ $\sqrt{{\mathit{x}}^2+\frac{1}{4}}$ + x = $\frac{1}{5}$ × 60 = 12
∴ ${\left(12+-\mathit{x}\right)}^2={\mathit{x}}^2+\frac{1}{4}$
⇒ 144 + ${\mathit{x}}^2$ - 24x = ${\mathit{x}}^2+\frac{1}{4}$
⇒ 24x = 144 - $\frac{1}{4}=\frac{575}{4}$
⇒ x = $\frac{575}{4\times 24}$ = 6 km