#### A passenger train of length 60 m travels at a speed of 80 km/hr. Another train of length 120 m travels at a speed of 30 km/hr . The ratio of times taken by the passenger train to completely cross the second train when : (i) they are moving in the same direction and (ii) when they are moving in the opposite direction isOption: 1 $\frac{25}{11}$Option: 2 $\frac{3}{2}$Option: 3 $\frac{5}{2}$Option: 4 $\frac{11}{5}$

The total distance to be traveled by the train is $\mathrm{60+120=180m}$

When the trains are moving in the same direction, relative velocity is

$v_1-v_2=80-30=50 \mathrm{kmh}^{-1}$

So, time taken to cross each other,

$t_1=\frac{180}{50 \times \frac{10^3}{3600}}=\frac{18 \times 18}{25} \mathrm{~s}$

When the trains are moving in the opposite direction, relative velocity is

$\left|v_1-\left(-v_2\right)\right|=80+30=110 k m h^{-1}$

So, the time taken to cross each other

$t_2=\frac{180}{110 \times \frac{1000}{3600}}=\frac{18 \times 36}{110} \mathrm{~s}$

Ratio, $\frac{t_1}{t_2}=\frac{\frac{18 \times 18}{25}}{\frac{18 \times 36}{110}}=\frac{11}{5}$