Problems on Trains Quiz Set 009

Let the ratio of their speeds by r. If the speed of one train is v, then the speed of the other is rv. By the speed and distance formula, the sum of their lengths is $(v × 19) + (rv × 65)$ which should equal the value obtained from the time they take to cross each other,i.e., $(v + rv) × 23)$. So $v × (19 + r × 65$ = $v × (1 + r) × 23).$ Cancelling v and solving for r we get ${2/21}$.

Let the speed of the train be v km/h. Distance travelled by this train in (4 + 12) hours = 16v km. Equating this to the distance travelled by the second train we get 16v = 20 × 4, which gives v = 5 km/h.

If they take $t_1 and t_2$ hours respectively to reach their destinations, then the ratio of their speeds is $√t_2 : √t_1$. So we get $√36 : √16$, which gives 6 : 4, or ${3/2}$.

The length of the train can be obtained from the time it takes to cross the pole. The length of the train = $14 × 18$ = 252m. To cross the platform it must travel a total distance equal to the combined lengths of the train and the platform at this speed. So time = ${252 + 1008}/14$ = 90 seconds.

Let the normal speed be x km/hr. We have been given $120/x$ - $120/{x + 12}$ = 5. This translates to the quadratic equation $5x^2 + 60x - 1440 = 0$, which can be solved to obtain x = 12 as the answer. If you don't want to solve the equation, then you can put each option into this equation and check that way. But this trick will work only if all the options have some numerical value.